# 2.5: Decimal Addition Using Front-End Estimation

**At Grade**Created by: CK-12

**Practice**Decimal Addition Using Front-End Estimation

Kim is packaging up some books to send to her brother who is studying abroad in Europe. She learns that the weight limit for the flat rate box she is using from the post office is 20 pounds. She has 4 books that she wants to send to her brother. The books weigh 5.431 pounds, 3.713 pounds, 4.1325 pounds, and 3.98 pounds. How can Kim estimate the total weight of the books she wants to send? Will she be able to send them in the flat rate box?

In this concept, you will learn how to estimate decimal sums using front-end estimation.

### Adding Decimals Using Front-End Estimation

To **estimate** means to find an approximate solution to a problem.

You can estimate a solution when you don’t need an exact answer, when you need to quickly get an idea of what an answer will be, or when you want to check if your exact answer is reasonable.

There are many different methods for estimation. One method is **front-end estimation**. Front-end estimation relies on adding the front-end digits (the left-most digits) of the numbers.

Here are the steps for front-end estimation with decimal number addition.

- Add the digits to the left of the decimal point (the whole numbers).
- Add the digits directly to the right of the decimal point (the digits in the tenths place).
- Add the results from steps 1 and 2.

Here is an example.

Use front-end estimation to estimate the sum of 6.819 and 4.621.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}6.819 \\ 4.621\end{align*}

Now, add the whole numbers.

\begin{align*}6+4=10\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.8+0.6=1.4\end{align*}

Finally, add the results.

\begin{align*}10+1.4=11.4\end{align*}

The answer is 6.819 plus 4.621 is approximately 11.4.

### Examples

#### Example 1

Earlier, you were given a problem about Kim, who is packaging up some books to send to her brother.

The weight limit for the box she is using is 20 pounds. The 4 books she wants to send weigh 5.431 pounds, 3.713 pounds, 4.1325 pounds, and 3.98 pounds. Kim needs to see if her books weigh less than the 20 pound limit.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}\begin{array}{rcl} & \ \ 5.431 \\ & \ \ 3.713 \\ & \quad 4.1325 \\ & 3.98 \end{array}\end{align*}

Now, add the whole numbers.

\begin{align*}5+3+4+3=15\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.4+0.7+0.1+0.9=2.1\end{align*}

Finally, add the results.

\begin{align*}15+2.1=17.1\end{align*}

The answer is that all together the books weigh about 17.1 pounds. Even though this is a slight underestimation of their weight, they definitely weigh under 20 pounds. Kim will be able to mail them in the box.

#### Example 2

Use front-end estimation to estimate the sum of 2.93474 and 9.72155.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}2.93474 \\ 9.72155\end{align*}

Now, add the whole numbers.

\begin{align*}2+9=11\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.9+0.7=1.6\end{align*}

Finally, add the results.

\begin{align*}11+1.6=12.6\end{align*}

The answer is 2.93474 plus 9.72155 is approximately 12.6.

#### Example 3

Use front-end estimation to estimate the sum of 3.5137 and 2.34.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}\begin{array}{rcl} & \quad 3.5137 \\ & 2.34 \end{array}\end{align*}

Now, add the whole numbers.

\begin{align*}3+2=5\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.5+0.3=0.8\end{align*}

Finally, add the results.

\begin{align*}5+0.8=5.8\end{align*}

The answer is 3.5137 plus 2.34 is approximately 5.8.

#### Example 4

Use front-end estimation to estimate the sum of 12.67194 and 8.1232.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}\begin{array}{rcl} & 12.67194 \\ & 8.1232 \end{array}\end{align*}

Now, add the whole numbers.

\begin{align*}12+8=20\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.6+0.1=0.7\end{align*}

Finally, add the results.

\begin{align*}20+0.7=20.7\end{align*}

The answer is 12.67194 plus 8.1232 is approximately 20.7.

#### Example 5

Use front-end estimation to estimate the sum of 15.67018 and 9.34523.

First, arrange the numbers vertically, lining up the decimal points.

\begin{align*}15.67018 \\ 9.34523\end{align*}

Now, add the whole numbers.

\begin{align*}15+9=24\end{align*}

Next, add the digits in the tenths place.

\begin{align*}0.6+0.3=0.9\end{align*}

Finally, add the results.

\begin{align*}24+0.9=24.9\end{align*}

The answer is 15.67018 plus 9.34523 is approximately 24.9.

### Review

Use front-end estimation to estimate the following sums.

- \begin{align*}4.57 + 2.34\end{align*}
- \begin{align*}2.123 + 4.136\end{align*}
- \begin{align*}8.913 + 2.047\end{align*}
- \begin{align*}8.7651 + 2.345\end{align*}
- \begin{align*}2.436 + 4.567\end{align*}
- \begin{align*}8.127 + 9.431\end{align*}
- \begin{align*}8.214 + 7.3214\end{align*}
- \begin{align*}12.137 + 2.456\end{align*}
- \begin{align*}18.671 + 20.41\end{align*}
- \begin{align*}21.643 + 22.123\end{align*}
- \begin{align*}18.012 + 19.367\end{align*}
- \begin{align*}21.456 + 18.023\end{align*}
- \begin{align*}0.48218 + 0.61927\end{align*}
- \begin{align*}6.7765 + 6.421192\end{align*}
- \begin{align*}0.5075412 + 0.859931 + 0.373462\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.5.

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Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.Front-End Estimation

Front-end estimation is a method of estimating where you only add the digits in the greatest place value.Rounding

Rounding is reducing the number of non-zero digits in a number while keeping the overall value of the number similar.### Image Attributions

In this concept, you will learn how to estimate decimal sums using front-end estimation.

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