Decimals for Nursing School Entrance Exam Study Guide

Changing Decimals to Fractions

To change a decimal to a fraction, write the digits of the decimal as the numerator and write the decimal's name as the denominator. Then reduce the fraction, if possible.

Example:   .018

1. Write 18 as the numerator:
2. Three places to the right of the decimal means thousandths, so write 1,000 as the denominator:
3. Reduce by dividing 2 into the numerator and denominator:

Comparing Decimals

Because decimals are easier to compare when they have the same number of digits after the decimal point, you can tack zeros onto the end of the shorter decimals without it affecting the number value. Then all you have to do is compare the numbers as if the decimal points weren't there:

Example: Compare 0.08 and 0.1.

1. Tack one zero at the end of 0.1:                               0.10
2. To compare 0.10 to 0.08, just compare 10 to 8.
3. Since 10 is larger than 8, 0.1 is larger than 0.08.

Adding and Subtracting Decimals

To add or subtract decimals, line them up so their decimal points are aligned. You may want to tack on zeros at the end of shorter decimals so you can keep all your digits lined up evenly. Remember, if a number doesn't have a decimal point, then put one at the right end of the number and add zeros after it.

Example: 1.23 + 57 + 0.038

1. Line up the numbers like this:	1.230
2. Add:	58.268

Example: 1.23 -?0.038

1. Line up the numbers like this:	1.230
2. Subtract:	1.192

Multiplying Decimals

To multiply decimals, ignore the decimal points and just multiply the numbers. Then count the total number of decimal digits (the digits to the right of the decimal point) in all of the numbers you are multiplying. Count off that total number of digits in your answer beginning at the right side and put the decimal point to the left of those digits.

Example: 215.7 × 2.4

1. Multiply 2157 times 24:
2. Because there are a total of two decimal digits in 215.7 and 2.4, count off two places from the right in 51768, placing the decimal point to the left of the last two digits:	517.68

If your answer doesn't have enough digits, tack zeros on to the left of the answer.

Example: 0.03 × 0.006

1. Multiply 3 times 6:                                                                                                 3 × 6 = 18
2. You need 5 decimal digits in your answer, so tack on 3 zeros:                                 00018
3. Put the decimal point at the front of the number (which is 5 digits in from the right):   0.00018

Dividing Decimals

To divide a decimal by a whole number, set up the division and immediately bring the decimal point straight up into the answer . Then divide as you would normally divide whole numbers:

Example:    

To divide any number by a decimal, there is an extra step to perform before you can divide. Move the decimal point to the very right of the number you're dividing by, counting the number of places you're moving it. Then move the decimal point the same number of places to the right in the number you're dividing into. In other words, first change the problem to one in which you're dividing by a whole number.

Example:

1. Because there are 2 decimal digits in 0.06, move the decimal point 2 places to the right in both numbers and move the decimal point straight up into the answer:
2. Divide using the new numbers:

Under certain conditions, you have to tack on zeros to the right of the last decimal digit in the number you are dividing into:

• If there aren't enough digits for you to move the decimal point to the right
• If you are dividing a whole number by a decimal. Then you will have to tack on the decimal point as well as some zeros.
• If the answer doesn't come out evenly when you do the division

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems