# Decimals Basics

• Decimals are based on the number ten.
• The basic units of the decimal system are 0 1 2 3 4 5 6 7 8 9 10.
• Many arithmetic problems produce an answer in decimal form.
• Zero is often used as a placeholder to the left of the decimal point —> 0.5 = .5
• There is an invisible decimal point to the right of any whole number —> 7. = 7

When asked to convert π, a fraction, or a square root to decimal form,
use the toggle button . is the decimal point command.

To convert a decimal to percent, move the decimal point two places to the right;
this maneuver is the same as multiplying the decimal by 100.
0.07 → 7.% = 7%
0.07 × 100 = 7%
0.70 → 70.% = 70%
0.70 × 100 = 70%

To convert percent to a decimal, move the invisible decimal point two places to the left; this maneuver is the same as dividing the percent by 100.
0.07 ← 7.% = 7%
7 ÷ 100 = 0.07
0.70 ← 70.% = 70%
70 ÷ 100 = 0.70

The decimal system positions digits as wholes (tens, hundred, thousands, etc.) and parts (tenths, hundredths, thousandths, etc.) of ten.

2146.8

thousands

2146.87

hundreds

2146.873
””’
””’tens

2146.873
”””’
”””’ones

2146.873
”””””’
”””””’tenths

2146.873
”””””””
””””””’ hundredths

2146.873
””””””””
””””””””thousandths

Question
Convert 0.08 to percent.

8%

To convert a decimal to percent, move the decimal point two places to the right.
0.08 → 8.% = 8%

Question
Convert 0.85 to percent.

85%

To convert a decimal to percent, move the decimal point two places to the right.
0.85 → 85.% = 85%

Question
Convert 6% to a decimal.

0.06

To convert percent to a decimal, move the invisible decimal point two places to the left.
0.06 ← 6.% = 6%

Question
Convert 65% to a decimal.

0.65

To convert percent to a decimal, move the invisible decimal point two places to the left.
0.65 ← 65.% = 65%

Question

What is 6.93 + 0.25?

7.18

Calculator Click What You See Comment blinker clears screen 93 + 0 25 6.93+0.25 Addition 7.18 Answer
###### Decimals

Question

What is 6.93 – 0.25?

6.68

Calculator Click What You See Comment blinker clears screen 93 – 0 25 6.93-0.25 Subtraction 6.68 Answer
###### Decimals

Question

What is 6.93 × 0.25?

1.7325

Calculator Click What You See Comment blinker clears screen 93 × 0 25 6.93*0.25 Multiplication 1.7325 Answer
###### Decimals

Question

What is 6.93 ÷ 0.25?

27.72

Calculator Click What You See Comment blinker clears screen 93 ÷ 0 25 6.93÷0.25 Division 27.72 Answer
###### Decimals

Question
Round the previous answer to the nearest tenth.

27.7

See Rounding.
27.72  27.7

Practice – Questions
1.  Convert 9% to a decimal.

2.  Convert 95% to a decimal.

3.  Convert 0.04 to percent.

4.  Convert 0.45 to percent.

5.  Convert 0.455 to percent.

6.  What is 3.94 + 0.33?

7.  What is 3.94 – 0.33?

8.  What is 3.94 × 0.33?

9.  What is 3.94 ÷ 0.33?

10.  With reference to Question 9, round your answer to the nearest hundredth.

1.  0.09

2.  0.95

3.  4%

4.  45%

5.  45.5%

6.  4.27

7.  3.61

8.  1.3002

9.  11.93939394

10.  11.94