DECIMALS: FAST FACTS

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One decimal place to the right of the decimal point is the "tenths" place, but one decimal place to the left of the decimal point is the "ones" place. The "tens" place is two places to the left.

(Scroll left to right to see a place value chart from millions to millionths, inclusive.  The decimal point lies between the ones place and the tenths place.  Note that all place value positions to the right of the decimal point have a "th" ending.)

Place Value Chart

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

tenths

hundredths

thousandths

ten thousandths

hundred thousands

millionths

To add and subtract decimals, line up the decimal points, use place-holding zeros.  Note:  Whole numbers are understood to have a decimal point to the right of the ones place.

When multiplying decimals, don't consider decimal places until the problem is solved. Count all places to the right of the decimal point in the problem. Count that number of places in the product (the answer) starting from the right.

Dividing Decimals:

If the number in a division box has a decimal, but the number outside of the division box does not have a decimal, place the decimal point in the quotient (the answer) directly above the decimal point in the division box.

If both the numbers inside and outside of the division box have decimals, count how many places are needed to move the decimal point outside of the division box (the divisor) to make it a whole number. Move the decimal point in the number inside of the division box  (the dividend) the same number of places. Place the decimal point in the quotient (the answer) directly above the new decimal point.

If the number outside of the division box has a decimal, but the number inside of the division box does not, move the decimal place on the outside number however many places needed to make it a whole number. Then to the right of the number in the division box (a whole number with an "understood decimal" at the end) add as many zeros to match the number of places the decimal was moved on the outside number. Place the decimal point in the quotient directly above the new decimal place in the division box.

Rounding Decimals:

To round a number to the nearest tenth (one place to the right of the decimal point), compute the number to the hundredths place (two places after the decimal) . If the number in the hundredths place is "five" or more , add "one" to the number in the tenths place and drop the number in the hundredths place. If the number in the hundredths place is under "five," leave the number in the tenths place as is and drop the number in the hundredths place.  

Round the following to the nearest tenth.

Therefore, to round a number to any decimal place, just compute the number one place value position farther to the right. The extra place is a gauge which indicates whether the number is close to what it reads (if the next number is less than "5") or is closer to one number higher (if the next number is "5" or more).

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