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Small Decimal Rounding to a Leading Digit

Round to the first non-zero digit of decimals less than 1.0.

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Estimate Decimal Products and Quotients Using Leading Digits

Have you ever had to figure out a dilemma involving money? Take a look at this situation.

The City Orchestra received a total of $1,891.50 in donations. This needs to be divided evenly among six different departments. How much will each department receive?

Use the information in this Concept to help you solve this problem using decimals and estimation.


To estimate products and quotients with decimals, you need to first round the numbers so that they are easier to work with. To round to the nearest whole number, look at the digit in the tenths place. If it is less than 5, round down. If it is 5 or greater, round up.

Remember that an estimate is an answer that is not exact, but is approximate and reasonable.

Take a look at this one.

Estimate the product: \begin{align*}11.256 \times 6.81\end{align*}11.256×6.81

First, we round the first number. Since there is a 2 in the tenths place, 11.256 rounds down to 11.

Now round the second number. Since there is an 8 in the tenths place, 6.81 rounds up to 7.

Now multiply the rounded numbers.

\begin{align*}11 \times 7 = 77\end{align*}11×7=77

A good estimate for the product is 77.

Here is another one.

Estimate the quotient: \begin{align*}91.93 \div 4.39\end{align*}91.93÷4.39

First we round the first number. Since there is a 9 in the tenths place, 91.93 rounds up to 92.

Now round the second number. Since there is a 3 in the tenths place, 4.39 rounds down to 4.

Now divide the rounded numbers.

\begin{align*}92 \div 4=23\end{align*}92÷4=23

A good estimate for the quotient is 23.

Did you notice which numbers we multiplied? We multiplied the whole digits or the digits that were leading the entire number. We did the same thing when we divided.

Yes. We work with the digits that are in the “lead”. With those digits, we can find a reasonable estimate.

Estimate by using leading digits

Example A

\begin{align*}4.237 \times 12.123\end{align*}4.237×12.123

Solution:  \begin{align*}48\end{align*}48

Example B

\begin{align*}16.123 \div 4.00012\end{align*}16.123÷4.00012

Solution:  \begin{align*}4\end{align*}4

Example C

\begin{align*}162.003 \times 2.137\end{align*}162.003×2.137

Solution:  \begin{align*}324\end{align*}324

Now let's go back to the dilemma from the beginning of the Concept.

Notice that the key word “each” tells us that we are going to need to divide. The money is being split up and that means division.

Divide to find the amount each department will receive: \begin{align*}1891.5 \div 6 = 315.25\end{align*}1891.5÷6=315.25

Each department will receive $315.25.

Guided Practice

Here is one for you to try on your own.

Estimate using leading digits.

\begin{align*}120.0045 \div 6.237\end{align*}120.0045÷6.237


First, we take only the leading digits and rewrite this problem.

\begin{align*}120 \div 6\end{align*}120÷6

Now our work is quite simple.

\begin{align*}120 \div 6 = 2\end{align*}120÷6=2

Our estimate is \begin{align*}2\end{align*}2.

Video Review

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Directions: Estimate each product or quotient by using leading digits.

1. \begin{align*}35.0012 \div 5.678\end{align*}35.0012÷5.678

2. \begin{align*}5.123 \times 11.0023\end{align*}5.123×11.0023

3. \begin{align*}12.0034 \div 4.0012\end{align*}12.0034÷4.0012

4. \begin{align*}12.123 \times 3.0045\end{align*}12.123×3.0045

5. \begin{align*}48.0012 \div 12.098\end{align*}48.0012÷12.098

6. \begin{align*}13.012 \times 3.456\end{align*}13.012×3.456

7. \begin{align*}33.234 \div 11.125\end{align*}33.234÷11.125

8. \begin{align*}12.098 \times 2.987\end{align*}12.098×2.987

9. \begin{align*}4.769 \times 8.997\end{align*}4.769×8.997

10. \begin{align*}14.98 \div 7.002\end{align*}14.98÷7.002

11. \begin{align*}24.56087 \div 8.0012\end{align*}24.56087÷8.0012

12. \begin{align*}45.098 \div 5.0098\end{align*}45.098÷5.0098

13. \begin{align*}9.0987 \times 9.0001\end{align*}9.0987×9.0001

14. \begin{align*}34.021 \times 4.012\end{align*}34.021×4.012

15. \begin{align*}21.0098 \times 2.0987\end{align*}21.0098×2.0987

16. \begin{align*}14.231 \times 3.7601\end{align*}14.231×3.7601

17. \begin{align*}144.0056 \div 12.0112\end{align*}144.0056÷12.0112

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Dividend In a division problem, the dividend is the number or expression that is being divided.
divisor In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression 152 \div 6, 6 is the divisor and 152 is the dividend.
Estimate To estimate is to find an approximate answer that is reasonable or makes sense given the problem.
Leading Digit The leading digit of a decimal number less than one is the first digit to the right of the decimal point that is not a zero.

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