# Decimals

Decimals are an extension of the base ten numeral system to fractions of ten (such as hundredths and thousandths). In this way they are a variation of fractions and percentages.

## Rules

Decimals are fractions of 10, 100, 1000, and so on.

You will have access to a calculator on the GRE but it is nonetheless important that you understand the concept of decimals.

.1 is equal to one tenth; .01 is equal to one hundredth; .001 is equal to one thousandth. Decimals are added and subtracted in the same way ordinary numbers are.

When multiplying decimals, multiply the numbers without decimals; then, push the decimal place to the right once for each time each multiplier is pushed to the right of the decimal.

.05 multiplied by .05 equals .0025, not .25. 6 multiplied by .9 is 5.4, while .6 multiplied by .9 is .54. When in doubt, check these on the calculator.

## Practice

1. What is .04 multiplied by .08?

2. y is equal to .4(x). If x equals 20, what does y equal?

3. What is the value of .009(.008)(.007)?

1. .0032

4(8) is 32. .04 and .08 are both pushed 2 points to the right of the decimal; thus, their product is pushed 4 points to the right.

2. 8

.4(20) = (20) = 8

3. 0.000000504.

The multipliers are each pushed to the right of the decimal 3 times. Thus, we take their product without decimals, and push it to the right 9 times.

9(8)(7) is 504; which pushed to the right 9 times equals 0.000000504.