5.2 Decimal Operations

Learning objectives

Learning objectives

• Add and subtract decimals

• Multiply decimals

• Divide decimals

• Use decimals in money applications

Add and Subtract Decimals

Let’s take one more look at the lunch order from the start of Decimals, this time noticing how the numbers were added together.

All three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal points lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimals this way, we can add or subtract the corresponding place values just as we did with whole numbers.

Example 5.11

Solution

1. Write the addends vertically. Place $3.7$ above $12.4$ with the decimal points directly above one another.
2. Check matching place values. Both numbers have one digit in the tenths place, so no extra placeholder zero is needed.
3. Add the tenths. The tenths digits are $7$ and $4$, and their sum $11$ contributes $1$ to the ones place.
4. Add the ones digits. The ones digits are $3$ and $2$, and $3+2+1$ from the carry gives $6$.
5. Place the decimal point. Put the decimal in the tenths column of the answer, giving $3.7+12.4=16.1$.

Takeaway: Adding $3.7$ and $12.4$ column by column produces $16.1$ when the tenths column and its carry are handled correctly.

Example 5.12

Solution

1. Write the numbers vertically. Rewrite $23.5$ as $23.50$ so that both numbers have two decimal places, and place the decimal points in the same column: $23.50$ above $41.38$. This agrees with the figure that highlights the added trailing zero in $23.50$.
2. Add the hundredths. The hundredths digits are $0$ and $8$, so write $8$ in the hundredths place of the answer.
3. Add the tenths. The tenths digits are $5$ and $3$, so $5+3=8$; write $8$ in the tenths place.
4. Add the ones. The ones digits are $3$ and $1$, so $3+1=4$; write $4$ in the ones place.
5. State the sum. The result is $64.88$, so $23.5+41.38=64.88$. The final figure displays this same sum after the decimal points have been aligned.

Takeaway: Aligning decimal points before adding ensures that every digit is added in the correct place-value column.

How much change would you get if you handed the cashier a $\text{\textdollar 20}$ bill for a $\text{\textdollar 14.65}$ purchase? We will show the steps to calculate this in the next example.

Example 5.13

Solution

1. Rewrite with matching places. Express $20$ as $20.00$ and set up $20.00-14.65$ vertically, as shown in the figure with the two zeros highlighted for borrowing.
2. Subtract the hundredths. Since $0$ is less than $5$, borrow one tenth from the tenths column, changing $0$ hundredths to $10$ hundredths; $10-5=5$.
3. Regroup the tenths. The tenths digit is now $9$, so $9-6=3$.
4. Subtract the remaining columns. In the ones column, borrow from the tens so that $10-4=6$. The tens column then gives $1-1=0$, so the aligned subtraction $20.00-14.65=5.35$ has zeros in the tens and ones places and $3$ in the tenths place.
5. State the result. The figure with crossed-out digits confirms that $20.00-14.65=5.35$, so $20-14.65=5.35$ dollars.

Takeaway: Borrowing across decimal columns is necessary when a smaller place value must be subtracted from a larger one.

Example 5.14

Solution

1. Compare the magnitudes. The expression $2.51-7.4$ subtracts the larger number $7.4$ from $2.51$, so its result must be negative.
2. Make the decimal places match. Write $7.4$ as $7.40$ and set up $7.40-2.51$, matching the figure that highlights the trailing zero in $7.40$.
3. Subtract the hundredths. The hundredths digit is $0-1$, so borrow from the tenths, changing $0$ to $10$; then $10-1=9$.
4. Complete the place-value subtraction. The tenths now give $3-5$, so borrow from the ones column, making them $13-5=8$; the ones give $6-2=4$.
5. State the signed result. The magnitude is $4.89$, but the original order requires a negative sign, so $2.51-7.4=-4.89$. The figures display the matching-column calculation and the magnitude $4.89$.

Takeaway: When the minuend is smaller than the subtrahend, subtract the magnitudes and place a negative sign on the result.

Multiply Decimals

Multiplying decimals is very much like multiplying whole numbers—we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first review multiplying fractions.

Do you remember how to multiply fractions? To multiply fractions, you multiply the numerators and then multiply the denominators.

So let’s see what we would get as the product of decimals by converting them to fractions first. We will do two examples side-by-side in Table 5.3. Look for a pattern.

Table

5.3

There is a pattern that we can use. In A, we multiplied two numbers that each had one decimal place, and the product had two decimal places. In B, we multiplied a number with one decimal place by a number with two decimal places, and the product had three decimal places.

How many decimal places would you expect for the product of $(0.01)(0.004)?$ If you said “five”, you recognized the pattern. When we multiply two numbers with decimals, we count all the decimal places in the factors—in this case two plus three—to get the number of decimal places in the product—in this case five.

Once we know how to determine the number of digits after the decimal point, we can multiply decimal numbers without converting them to fractions first. The number of decimal places in the product is the sum of the number of decimal places in the factors.

The rules for multiplying positive and negative numbers apply to decimals, too, of course.

When you multiply signed decimals, first determine the sign of the product and then multiply as if the numbers were both positive. Finally, write the product with the appropriate sign.

Example 5.15

Solution

1. Count the decimal places. The factor $4.075$ has three decimal places and $3.9$ has one, so the product needs $3+1=4$ decimal places.
2. Separate the multiplier. Write $3.9=3+0.9$. Then $4.075\times0.9=3.6675$ and $4.075\times3=12.225$.
3. Align the decimal points. Write the second product as $12.2250$, and add the two partial products with their decimal points aligned: $\begin{array}{r}3.6675\\+12.2250\\\hline15.8925\end{array}$.
4. Connect the work to the figures. The earlier figures show the whole-number partial products $36675$ and $12225$ before the decimal point is placed; the final figure shows the same multiplication with the decimal point moved four places from the right.
5. State the product. The aligned addition gives $(3.9)(4.075)=15.8925$, agreeing with the final figure.

Takeaway: The decimal point in a decimal product goes as many places from the right as the combined decimal places of the factors.

Example 5.16

Solution

1. Count the decimal places. The factor $-8.2$ has one decimal place and $5.19$ has two, so the product must have three decimal places.
2. Multiply the magnitudes. The whole-number product is $8.2$ times $5.19$ in digits: $82\times519=42618$, so the magnitude before placing the decimal is $42618$.
3. Track the sign. The first factor is negative and the second is positive, so the product must be negative.
4. Place the decimal point. Move the decimal point three places from the right in $42618$ to obtain $42.618$, as indicated by the figure that shows the three-place rule.
5. State the result. Combining the negative sign with the magnitude gives $(-8.2)(5.19)=-42.618$.

Takeaway: Add the decimal places of both factors, place that many decimal places in the product, and keep the sign from the factors.

In the next example, we’ll need to add several placeholder zeros to properly place the decimal point.

Example 5.17

Solution

1. Count the decimal places. The factor $0.03$ has two decimal places and $0.045$ has three, so the product needs $2+3=5$ decimal places.
2. Write the vertical multiplication. Set up $0.045$ above $0.03$, as shown in the first figure, and multiply the digits without decimal points to obtain $45\times3=135$.
3. Account for the decimal positions. Since the unscaled product $135$ must become a number with five decimal places, write the needed placeholder zeros before it.
4. Place the decimal point. Moving five places from the right in $135$ gives $0.00135$, which agrees with the final figure and its blue counting arrow.
5. State the result. The product is $(0.03)(0.045)=0.00135$, and the intermediate figures show why five decimal places are required.

Takeaway: Placeholder zeros help you place the decimal point when multiplying decimals with several decimal places.

Multiply by Powers of $10$

In many fields, especially in the sciences, it is common to multiply decimals by powers of $10.$ Let’s see what happens when we multiply $1.9436$ by some powers of $10.$

Look at the results without the final zeros. Do you notice a pattern?

$\,\begin{array}{lcl} 1.9436(10) & = & 19.436 \\ 1.9436(100) & = & 194.36 \\ 1.9436(1000) & = & 1943.6 \\ \end{array}$

The number of places that the decimal point moved is the same as the number of zeros in the power of ten. Table 5.4 summarizes the results.

Table

5.4

We can use this pattern as a shortcut to multiply by powers of ten instead of multiplying using the vertical format. We can count the zeros in the power of $10$ and then move the decimal point that same of places to the right.

So, for example, to multiply $45.86$ by $100,$ move the decimal point $2$ places to the right.

Sometimes when we need to move the decimal point, there are not enough decimal places. In that case, we use zeros as placeholders. For example, let’s multiply $2.4$ by $100.$ We need to move the decimal point $2$ places to the right. Since there is only one digit to the right of the decimal point, we must write a $0$ in the hundredths place.

Example 5.18

Solution

1. Multiply by $10$. Move the decimal point in $5.63$ one place to the right to obtain $56.3$, so $5.63\times10=56.3$.
2. Multiply by $100$. Move the decimal point two places to the right to obtain $563$, so $5.63\times100=563$.
3. Multiply by $1000$. Move the decimal point three places to the right to obtain $5630$, so $5.63\times1000=5630$.
4. Connect the movements to the figures. The blue arrows in the three figures point upward from $5.63$, indicating the rightward shifts that occur as the multiplying factor grows.
5. State the three results. The products are $56.3$, $563$, and $5630$ for factors of $10$, $100$, and $1000$, respectively.

Takeaway: Multiplying by a power of ten moves the decimal point right by exactly as many places as the factor contains zeros.

Divide Decimals

Just as with multiplication, division of decimals is very much like dividing whole numbers. We just have to figure out where the decimal point must be placed.

To understand decimal division, let’s consider the multiplication problem

Remember, a multiplication problem can be rephrased as a division problem. So we can write

We can think of this as “If we divide 8 tenths into four groups, how many are in each group?” Figure 5.5 shows that there are four groups of two-tenths in eight-tenths. So $0.8\mathrm{÷}4=0.2.$

Using long division notation, we would write

Notice that the decimal point in the quotient is directly above the decimal point in the dividend.

To divide a decimal by a whole number, we place the decimal point in the quotient above the decimal point in the dividend and then divide as usual. Sometimes we need to use extra zeros at the end of the dividend to keep dividing until there is no remainder.

Example 5.19

Solution

1. Set up the division. Write $0.12\div3$ in long-division form, placing the quotient decimal above the decimal point of $0.12$, as shown in the figure.
2. Find the tenths digit. The $1$ in the tenths place is less than the divisor $3$, so write $0$ in the tenths place of the quotient and bring down the $2$ in the hundredths place.
3. Divide the hundredths. The brought-down value is $12$ hundredths, and $12\div3=4$, so write $4$ in the hundredths place with no remainder.
4. Check the place values. With the decimal points aligned, the dividend can be written as $0.120$ and the quotient as $0.040$, confirming that the $4$ is in the hundredths place.
5. State the result. The quotient is $0.04$, so $0.12\div3=0.04$, matching the completed long-division figure.

Takeaway: In long division of decimals, place the quotient decimal directly above the decimal point of the dividend.

In everyday life, we divide whole numbers into decimals—money—to find the price of one item. For example, suppose a case of $24$ water bottles cost $\text{\textdollar 3.99}.$ To find the price per water bottle, we would divide $\text{\textdollar 3.99}$ by $24,$ and round the answer to the nearest cent (hundredth).

Example 5.20

Solution

1. Set up the division. Write $3.99\div24$ in long-division form and place the quotient decimal above the $3$, as in the first figure.
2. Start with the whole-number part. Since $3$ is less than $24$, write $0$ in the ones place of the quotient and bring down the next digit to form $39$.
3. Work through the decimal digits. $39\div24=1$ with remainder $15$; bringing down the next digit forms $159$, and $159\div24=6$ with remainder $15$; bringing down the final zero forms $150$, and $150\div24=6$ with remainder $6$.
4. Round to a cent. Continuing gives the quotient $0.16625$ shown in the second figure, and since the third decimal digit is $6$, the hundredths digit rounds from $6$ to $7$.
5. State the result. Jessie pays about $17$ cents for each bottle, so $3.99\div24=0.16625$ rounds to $0.17$.

Takeaway: Divide the total cost by the number of equal items, then round the unit price to the nearest cent.

Divide a Decimal by Another Decimal

So far, we have divided a decimal by a whole number. What happens when we divide a decimal by another decimal? Let’s look at the same multiplication problem we looked at earlier, but in a different way.

Remember, again, that a multiplication problem can be rephrased as a division problem. This time we ask, “How many times does $0.2$ go into $0.8\mathrm{?"}$ Because $(0.2)(4)=0.8,$ we can say that $0.2$ goes into $0.8$ four times. This means that $0.8$ divided by $0.2$ is $4.$

We would get the same answer, $4,$ if we divide $8$ by $2,$ both whole numbers. Why is this so? Let’s think about the division problem as a fraction.

We multiplied the numerator and denominator by $10$ and ended up just dividing $8$ by $2.$ To divide decimals, we multiply both the numerator and denominator by the same power of $10$ to make the denominator a whole number. Because of the Equivalent Fractions Property, we haven’t changed the value of the fraction. The effect is to move the decimal points in the numerator and denominator the same number of places to the right.

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

It may help to review the vocabulary for division:

Example 5.21

Solution

1. Recognize the negative sign. The quotient $-2.89\div3.4$ is negative because the dividend is negative and the divisor is positive.
2. Clear the divisor's decimal. Multiply both numbers by $10$, which gives $-28.9\div34$ without changing the quotient's value. Writing the dividend as $28.90$ shows the same aligned long division used in the figure.
3. Divide the whole-number part. Since $28$ is less than $34$, write $0$ in the ones place of the quotient and continue with the decimal digits.
4. Complete the division. Bring down $9$ to get $289$, and $289\div34=8$ with remainder $17$. Bring down the zero, and $170\div34=5$ with remainder $0$, so the quotient is $0.85$, as the completed figure shows.
5. State the result. Restore the negative sign to obtain $-2.89\div3.4=-0.85$, agreeing with the quotient $0.85$ shown for the positive magnitudes.

Takeaway: Shift both decimal points the same number of places to clear the divisor, and preserve the sign of the quotient.

Example 5.22

Solution

1. Simplify the signs. Both $25.65$ and $0.06$ are positive, so the quotient $-25.65\div(-0.06)$ is positive.
2. Clear the divisor's decimal. Move both decimal points two places right, changing the calculation to $2565\div6$, as shown by the blue arrows in the first figure.
3. Divide the whole numbers. Compute $2565\div6=427$ with remainder $3$, and append the decimal fraction $3/6=0.5$ to obtain $427.5$.
4. Check the place-value scale. The second figure displays the same long division and confirms the quotient $427.5$ for the cleared numbers.
5. State the result. Because the two negatives cancel, $(-25.65)\div(-0.06)=427.5$.

Takeaway: Dividing decimals becomes whole-number division after the decimal points in both numbers are shifted equally.

Now we will divide a whole number by a decimal number.

Example 5.23

Solution

1. Choose a common shift. The divisor $0.05$ has two decimal places, so multiply both $4$ and $0.05$ by $100$.
2. Rewrite the division. The equivalent calculation is $400\div5$, while the original expression remains $4\div0.05$.
3. Divide the whole numbers. Since $400\div5=80$, the quotient is $80$; the second figure shows the same division with $40\div5=8$ followed by the final zero.
4. Check the scale. Moving both decimal points two places right preserves the quotient, so no additional decimal placement is needed.
5. State the result. The answer is $4\div0.05=80$, which can also represent the $80$ nickels contained in $4$.

Takeaway: Shifting both decimal points the same number of places preserves a quotient and makes the divisor a whole number.

Use Decimals in Money Applications

We often apply decimals in real life, and most of the applications involving money. The Strategy for Applications we used in The Language of Algebra gives us a plan to follow to help find the answer. Take a moment to review that strategy now.

Example 5.24

Solution

1. Identify the starting amount. Paul received $50$, which is the amount from which the purchase must be subtracted.
2. Identify the amount spent. The video game cost $31.64$, so the remaining amount is $50-31.64$.
3. Align the money amounts. Write $50$ as $50.00$ and place it above $31.64$ with the decimal points aligned.
4. Subtract by place value. Borrowing as needed gives $50.00-31.64=18.36$.
5. Check the result. Since $18.36$ is less than $50$ and adding $31.64$ returns $50.00$, Paul has $18.36$ left.

Takeaway: Subtracting Paul's $31.64$ purchase from $50.00$ leaves the verified balance of $18.36$ dollars.

Example 5.25

Solution

1. Choose the cost expression. Eight gallons at $3.529$ per gallon gives the expression $8(3.529)$ dollars.
2. Multiply the gallons and unit price. Multiplying the decimal by $8$ gives $8(3.529)=28.232$ dollars before rounding.
3. Identify the rounding place. The hundredths digit in $28.232$ is $3$, and the thousandths digit is $2$.
4. Round to the nearest cent. Since the thousandths digit $2$ is less than $5$, keep the hundredths digit unchanged and obtain $28.23$.
5. Check the reasonableness. Eight gallons at about $3.53$ each must cost about $28$, and $28.23$ is consistent with that estimate.

Takeaway: The unrounded fuel cost is $28.232$ dollars, so the nearest-cent charge for eight gallons is $28.23$.

Example 5.26

Solution

1. Identify the equal share. The $31.76$ dinner total must be divided equally among four friends.
2. Write the division expression. Each share is represented by $31.76\div 4$ dollars.
3. Divide the dollars. Performing the division gives $31.76\div 4=7.94$ for each friend.
4. Check by multiplying. Four equal shares must reproduce the total, and $4(7.94)=31.76$.
5. State the answer. Each friend should pay $7.94$ for his share of the dinner.

Takeaway: Dividing the $31.76$ bill equally among four friends gives $7.94$ per person, as confirmed by multiplying back.

Be careful to follow the order of operations in the next example. Remember to multiply before you add.

Example 5.27

Solution

1. Find the banana cost. Multiply $6$ bananas by $0.22$ dollars each to get $6(0.22)=1.32$ dollars.
2. Find the orange cost. Multiply $4$ oranges by $0.49$ dollars each to get $4(0.49)=1.96$ dollars.
3. Write the combined expression. The total cost is $1.32+1.96$ dollars because both item costs must be included.
4. Add the aligned amounts. With the decimal points aligned, the hundredths are $2+6=8$ and the tenths are $3+9=12$, giving $3.28$ dollars.
5. Check the total. The fruit bill is greater than either item subtotal and equals $3.28$ dollars, so Marla pays $3.28$.

Takeaway: The banana subtotal $1.32$ plus the orange subtotal $1.96$ gives Marla a total fruit cost of $3.28$ dollars.

Section 5.2 Exercises

Section 5.2 Exercises

Add and Subtract Decimals

In the following exercises, add or subtract.

Multiply Decimals

In the following exercises, multiply.

Divide Decimals

In the following exercises, divide.

Mixed Practice

In the following exercises, simplify.

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Everyday Math

Writing Exercises

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

1. Subtract: $4.77-6.3.$

2. Subtract: $8.12-11.7.$

3. Multiply: $(4.63)(-2.9).$

1. Multiply: $(-7.78)(4.9).$

2. Multiply $2.58$ by factors of ⓐ $\,10$ ⓑ $\,100$ ⓒ $\,1000.$

3. Multiply $14.2$ by factors of ⓐ $\,10$ ⓑ $\,100$ ⓒ $\,1000.$

1. Divide: $\text{\textdollar 6.99}\mathrm{÷}36.$

2. Divide: $\text{\textdollar 4.99}\mathrm{÷}12.$

3. Divide: $-1.989\mathrm{÷}5.1.$

1. Hector put $13$ gallons of gas into his car. One gallon of gas costs $\text{\textdollar 3.175}.$ How much did Hector owe for the gas? Round to the nearest cent.

2. Christopher bought $5$ pizzas for the team. Each pizza cost $\text{\textdollar 9.75}.$ How much did all the pizzas cost?

3. Six friends went out for dinner. The total cost of their dinner was $\text{\textdollar 92.82}.$ If they divide the bill equally, how much should each friend pay?

1. Chad worked $40$ hours last week and his paycheck was $\text{\textdollar 570}.$ How much does he earn per hour?

2. Suzanne buys $3$ cans of beans that cost $\text{\textdollar 0.75}$ each and $6$ cans of corn that cost $\text{\textdollar 0.62}$ each. How much is the total cost of these groceries?

3. Lydia bought movie tickets for the family. She bought two adult tickets for $\text{\textdollar 9.50}$ each and four children’s tickets for $\text{\textdollar 6.00}$ each. How much did the tickets cost Lydia in all?

1. $18.37+9.36$

2. $21.76-30.99$

3. $-16.53-24.38$

1. $-38.69+31.47$

2. $-4.2+(-9.3)$

3. $72.5-100$

1. $2.51-7.4$

2. $\mathrm{(-4.3)(2.71)}$

3. $(55.2)(1,000)$

1. $\text{\textdollar 8.49}\mathrm{÷}12$

2. $\text{\textdollar 117.25}\mathrm{÷}48$

3. $1.44\mathrm{÷}(-0.3)$

1. $\text{\textdollar 45}+0.08(\text{\textdollar 45})$

2. $[\text{\textdollar 75.42}+0.18(\text{\textdollar 75.42})]\mathrm{÷}5$

3. Spending money Brenda got $\text{\textdollar 40}$ from the ATM. She spent $\text{\textdollar 15.11}$ on a pair of earrings. How much money did she have left?

1. Shopping Adam bought a t-shirt for $\text{\textdollar 18.49}$ and a book for $\text{\textdollar 8.92}$ The sales tax was $\text{\textdollar 1.65}.$ How much did Adam spend?

2. Coupon Emily bought a box of cereal that cost $\text{\textdollar 4.29}.$ She had a coupon for $\text{\textdollar 0.55}$ off, and the store doubled the coupon. How much did she pay for the box of cereal?

3. Diet Leo took part in a diet program. He weighed $190$ pounds at the start of the program. During the first week, he lost $4.3$ pounds. During the second week, he had lost $2.8$ pounds. The third week, he gained $0.7$ pounds. The fourth week, he lost $1.9$ pounds. What did Leo weigh at the end of the fourth week?

1. Coffee Noriko bought $4$ coffees for herself and her co-workers. Each coffee was $\text{\textdollar 3.75}.$ How much did she pay for all the coffees?

2. Income Mayra earns $\text{\textdollar 9.25}$ per hour. Last week she worked $32$ hours. How much did she earn?

3. Hourly Wage Alan got his first paycheck from his new job. He worked $30$ hours and earned $\text{\textdollar 382.50}.$ How much does he earn per hour?

1. Restaurant Jeannette and her friends love to order mud pie at their favorite restaurant. They always share just one piece of pie among themselves. With tax and tip, the total cost is $\text{\textdollar 6.00}.$ How much does each girl pay if the total number sharing the mud pie is

ⓐ $\,2?$

ⓑ $\,3?$

ⓒ $\,4?$

ⓓ $\,5?$

ⓔ $\,6?$

2. Fast Food At their favorite fast food restaurant, the Carlson family orders $4$ burgers that cost $\text{\textdollar 3.29}$ each and $2$ orders of fries at $\text{\textdollar 2.74}$ each. What is the total cost of the order?

3. Zoo The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost $\text{\textdollar 29.95}$ and children’s tickets cost $\text{\textdollar 19.95}.$ What will the total cost be for $4$ adults and $7$ children?

1. Divide: $-2.04\mathrm{÷}5.1.$

2. Nicole earned $\text{\textdollar 35}$ for babysitting her cousins, then went to the bookstore and spent $\text{\textdollar 18.48}$ on books and coffee. How much of her babysitting money was left?

3. Amber bought a pair of shoes for $\text{\textdollar 24.75}$ and a purse for $\text{\textdollar 36.90}.$ The sales tax was $\text{\textdollar 4.32}.$ How much did Amber spend?

1. Paycheck Annie has two jobs. She gets paid $\text{\textdollar 14.04}$ per hour for tutoring at City College and $\text{\textdollar 8.75}$ per hour at a coffee shop. Last week she tutored for $8$ hours and worked at the coffee shop for $15$ hours.

ⓐ How much did she earn?

ⓑ If she had worked all $23$ hours as a tutor instead of working both jobs, how much more would she have earned?

2. At the 2010 winter Olympics, two skiers took the silver and bronze medals in the Men's Super-G ski event. Miller's time was $1$ minute $30.62$ seconds and Weibrecht's time was $1$ minute $30.65$ seconds. Find the difference in their times and then write the name of that decimal.