6th Grade Math Textbook, Fundamentals

 &KDSWHU

4-7

Update your skills. See page 411 X.

Estimate Decimal Products

and Quotients

Objective To estimate decimal products and quotients by using rounding,

compatible numbers, and powers of 10

A scientist in a pharmaceutical lab wants to change a
dilution of 0.0057 of a certain chemical to one that is
about 0.08 times as strong. What new dilution of the
chemical will approximate the dilution she wants?

You can round to estimate the product of two decimals

that are each less than 1.

Estimate: 0.0057 • 0.08

0.0057 • 0.08 Round each factor to its greatest nonzero place.

0.0057 0.006 7 5, so 0.005 rounds to 6 thousandths.

0.08 0.08 0.08 stays as 8 hundredths.

Multiply: 0.006• 0.080.000 48

So a dilution of 0.00048 will approximate the desired dilution.

You can also round to estimate the product of decimals when one

factor is greater than 1 and one factor is less than 1.

Estimate: 2500.35 • 0.036

2500.35 • 0.036 Round each factor to its greatest nonzero place.

2500.35 3000 5 5, so 2000 rounds to 3 thousands.

0.036 0.04 6 5, so 0.03 rounds to 4 hundredths.

Multiply: 3000 • 0.04120.00

So 2500.35 • 0.036 120.

You can use compatible numbersto estimate the

quotient of two decimals that are each greater than 1.

Estimate: 310.2 4.19

Write the nearest compatible whole numbers 310.2 320

for the dividend and divisor. 4.19 4

Divide: 320  4  80

So 310.2 4.19 80.

Count the decimal places in both factors.

Show the same number of decimal places

in the product as there are in the two factors combined.

You need the same number

of decimal places in the product as

there are in the two factors combined.

Think

The greatest nonzero

place in a number is

the place farthest to

the left that has a digit

that is not zero.

are numbers

that are easy to compute mentally.

Compatible numbers

Think

Use a division fact:

32  4  8

Even though 310.2

could round to 310,

use 320 because it

can be divided

evenly by 4.