Pre Algebra Decimals

PRE ALGEBRA DECIMALS

PRE Algebra Decimals
Place Value, Rounding, Adding, Subtracting, Multiplying, Fractions

Decimals Place Value

Decimals have a 'Place Value'.

Any number after the decimal is read by it's place value.

The first place value is Tenths, then Hundredths, Thousands, Ten Thousands, Hundred Thousands, Millions
Any number before the decimal is read as a number

EXAMPLE

. |TENTHS | HUNDREDTHS | THOUSANDS | TEN THOUSANDS | HUNDRED THOUSANDS | MILLIONS |

15. 4 6 1 is a decimal

All numbers after the decimal .461 are read with their place value
To read a decimal, you name the place value of the last number, in this example 1 is the last number
1 is in the third place, and we know the third place is Thousands
To read this decimal - say or write: fifteen and four hundred sixty one thousands

You use the last number's place value when reading or writing the decimal
If there is a number before the decimal, you use AND: and say or write, as this example - fifteen and

FYI: You could also be asked to Name the decimal, meaning read or write the decimal.

Practice Place Value

Write (name) the Decimal

PRACTICE:

14.23
13.14
1413.143
10.1253

ANSWERS
14.23
Answer: fourteen and twenty three hundredths

13.14
Answer:thirteen and fourteen hundredths

1413.143
Answer: one thousand four hundred thirteen and one hundred forty three thousands

10.1253
Answer: ten and one thousand two hundred fifty three ten thousands

Rounding Decimals

Decimals can be rounded by using the 'rule of rounding'.

If the number you are rounding is 4 or less, then keep the number as is.
If the number you are rounding is greater than 4, or 5 or more, change it to the next number
When rounding 'decimals', you may be asked to round to the "place value' of the decimal: such as Tenths, Hundredths, Thousandths, Ten Thousandths, Hundred Thousandths, Millions

For Example

If you are asked to round to the 'thousandths':
Decimal .67812, in this example the 8 is in the 'thousandths' place: Look at the number to the right of that number, Is the 1, 5 or greater, ?, no it is not, so you leave the 8 as it and remove all digits to its right
The answer is: .678

Practice:

Round each number to the 'place value' indicated

0.538 to the tenths
.245223 to the ten thousandths
.19436834 to the millions
.15361 to the thousandths

ANSWERS
0.538
As we need to round to the place of tenths; 5 is in the tenths place, so we look at 3, it is less than 5 so we do not round up the 5, and then we remove all digits after the 5 also.
Answer is .5

.245223
2 is in the ten thousandths place, so we look at 2, it is less than 5, so we do not round up the 2, and we remove all digits after the 2 also
Answer is .2452

.19436834
8 is in the millions place, so we look at 3, it is less than 5, so we do not round up the 8, and we remove all the digits after the 8
Answer is .194368

.15361
3 is in the thousandths place, so we look at 6, it is greater than 5, so we do round up the 3, it will be 4, and we remove all digits to the right of it
Answer: .154

Adding Decimals

To add decimals, line the decimals, then solve the problem, add zeros if needed.

PRACTICE:

13.4 + 123.45=
14.6 + 2.78=

ANSWERS:

123.45
+13.40
---------
136.85

14.60
+4.78
---------
19.38

Subtracting Decimals

To subtract decimals, line the decimals, then solve the problem. Add zeros if you need to.

EXAMPLE

16.7
-3.877
-------
16.700< Add zeros here, then solve the problem
-3.877
-------
12.823

Multiplying Decimals

To multiply decimals, multiply the numbers and then add the decimal, as per the decimal spaces in the numbers.

EXAMPLE:

12.2 x 11.9 =
First multiply 122 x 119 = 14518
145.18
Then add the decimals places, 1 decimal for 12.2 and 1 decimal for 11.9, count two decimal places from the left and add the decimal.

PRACTICE:

123.154 x 23.47 =
16.19 x 75.24 =
1 x 1.1 =

ANSWERS

123.154 x 23.1 =
2890.42438

16.19 x 75.24 =
1218.1356

1 x 1.1 =
1.1

Compare Decimals

PRACTICE:

Compare Decimals
.25 .124
.521 .8213
.6 .7

ANSWERS

.25 .124 Answer .25
.521 .8213 Answer .8213
.6 .7 Answer .7

PRACTICE:

Fractions To Decimals
1/3
1/9
2/3
4/1
1/25

ANSWERS

1/3 Answer .33
1/9 Answer .11
2/3 Answer .66
4/1 Answer .25
1/25 Answer .04

PRACTICE:

Decimals To Fractions
.02
.342
.1
.8
.21

ANSWERS

.02 Answer 2/100
.342 Answer 342/1000
.1 Answer 1/10
.9 Answer 8/10
.21 Answer 21/100

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