# Converting among decimals, fractions, and percents

### Converting among decimals, fractions, and percents

In this section, we estimate percents as fractions and as decimals. When converting between percents, fractions, and decimals, we reference the place value system, first introduced in the previous section. For example, in the decimal number 0.34, we have 3 tenths and 4 hundredths, which can be expressed as, $\frac{3}{10}$+$\frac{4}{100}$. 0.34 can also be expressed as 30 hundredths and 4 hundredths, which can be written as $\frac{30}{100}$+$\frac{4}{100}$=$\frac{34}{100}$. We also discuss how "cent" in the word "percent" refers to "hundred" . $\frac{34}{100}$ means 34 per 100 or 34 per cent. Along with the place value system, we use loading – strip models to convert between percents, fractions, and decimals.

#### Lessons

• Introduction
a)
How to convert between fractions and decimals?
• what is a fraction?
• convert fractions to decimals
• convert decimals to fractions

• 1.
Fill in the blank below.
a)
$\frac{3}{10}=\frac{ \Box }{100}=$____%

b)
$\frac{1}{4}=\frac{ \Box }{100}=$____%

c)
$\frac{7}{5}=\frac{ \Box }{100}=$____%

• 2.
Fill in the blank with the inequality >, < or = to make the statement true.
a)
10%___0.3

b)
$\frac{9}{8}$___100%

c)
4.5___$\frac{6}{10}$

• 3.
There are 20 people in the room below. What percent of people are the following colours?

a)
Red

b)
Orange

c)
Blue

• 4.
The table shows the number of boys and girls in a school who play soccer.
 Play soccer Total population Girls 64 510 Boys 128 500 Total 192 1010

a)
Estimate the percent of girls who play soccer. Then, calculate the percent using a calculator and round to the nearest tenth.

b)
Estimate the percent of boys who play soccer. Then, calculate the percent using a calculator and round to the nearest tenth.

c)
Estimate what percent of all the students who play soccer are girls. Then, calculate the percent using a calculator and round to the nearest tenth.