Core Focus on Decimals& Fractions

Estimating with Decimals

Lesson 1.5

Warm-Up1. Round 4.59 to the nearest whole number.

2. Round 123.48 to the nearest whole number.

3. Round $3.90 to the nearest dollar.

5

123

$4.00

Estimating with Decimals

Estimate sums, differences, products or quotients of expressions involving decimals.

Lesson 1.5

Good to Know! There are situations where using an estimate makes more sense than using

an exact value.

Example:Washington County could publish the following information:

The number of students in Washington County Schools probably changes every day because students move in and out of the county, so 10,500 is likely an estimate. The number of schools does not change often, so this is an exact statement.

Example:It is confusing to say that the average American family has 2.4 children. Instead, it is often said that the average American family has about two children.

The most common method for estimating decimal expressions is to round to the nearest whole number before calculating.

There are 10,500 students in the county.Washington County has 28 public schools.

Example 1The Oregon State bird, the Western Meadowlark,weighs between 3.18 and 5.3 ounces. Estimate thedifference between the heaviest weight and thelightest weight given.

Use rounding to estimate the difference. 5.3 – 3.18

Round each number to the nearest 5.3 → 5whole number. 3.18 → 3

Subtract. 5 – 3 = 2

The difference between the weights is about 2 ounces.

Example 2Apples cost $1.97 per pound. Ieysha buys a bag of apples that weighs 4.7 pounds. About how much money did Ieysha need to purchase the apples?

Use rounding to estimate the product. $1.97 × 4.7

Round each number to the nearest $1.97 → $2whole number. 4.7 → 5

Multiply. $2 × 5 = $10

Ieysha needed about $10.00 to purchase her apples.

VocabularyCompatible NumbersNumbers that are easy to mentally compute.

Good to Know!Compatible numbers can be used when estimating quotients.

1. Round the divisor to the nearest whole number.

2. Change the dividend to the nearest multiple of the new divisor.

This makes the two numbers compatible, or easy to compute mentally.

Example 3Maris saved $121.28 to buy board games for her nieces and nephews. The board games she bought cost around $19.95 each. Approximately how many board games did she buy?

Use compatible numbers to estimate. 121.28 ÷ 19.95

Round the divisor the nearest 121.28 ÷ 20whole number.

Change the dividend to the nearest 120 ÷ 20 = 6multiple of the new divisor.

Maris bought about six board games.

Communication PromptHow do you decide whether to round or use compatible numbers when estimating with decimals?

Exit ProblemsEstimate the answers to the following problems by rounding.

1. 5.79 + 2.8

2. 98.35 – 94.97

3. 6.32 × 8.75

Estimate the answers to the following problems by usingcompatible numbers.

4. 9.934 ÷ 2.14

5. 134.32 ÷ 4.88

9

3

54

5

27