User:MathMan64~enwikibooks/Arithmetic/Notation

Notation

Place value

The place value notational system, uses values for each digit that are multiples of ten.

Whole numbers

For whole numbers, the digit on the right is the ones. Moving to the left, the value of each place increases by multiplying ten: the tens place, hundreds, thousands, ten thousands, hundred thousands, millions, etc.

Examples

In 4932

• 2 is in the ones place.
• 3 is in the tens place.
• 9 is in the hundreds place.
• 4 is in the thousands place.

Each group of three digits is separated off by commas, and contains a ones, a tens and a hundreds place. The group on the right has no additional name. The next group to the left is the thousands group, and each place in that group ends with the word thousands. The group to the left of thousands is millions.

In 24,685,000

• There are zeros in the ones, tens, and hundreds places.
• 5 is in the thousands place.
• 8 is in the ten thousands place.
• 6 is in the hundred thousands place.
• 4 is in the millions place.
• 2 is in the ten millions place.

To the left of millions is billions, then trillions, and quadrillions. (This is the usage in the USA and most English speaking countries. Parts of Europe use a slightly different system for the names of the places larger than hundred millions.)

In 4,720,000,000,000

• There are zeros in the ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, and billions places.
• 2 is in the ten billions place.
• 7 is in the hundred billions place.
• 4 is in the trillions place.

Decimals

For indicating places smaller than one, a dot or decimal point is put to the right of the ones place. Each place to the right is decreased by dividing by ten. Assigning place values to the digits on the right of the decimal point starts next to the decimal point with tenths and moves to the right with each place value name. The place on the right of the tenths is the hundredths, then thousandths, ten thousandths, etc.

Notice that each decimal place value name is similar to a whole number place name, except that these decimal names all end in ths.

Also notice that there is no place on the right of the decimal point that is similar to the ones place just to the left of the decimal point. The ones place and the decimal point are the middle of this system.

Examples

In 0.5931

• 5 is in the tenths place.
• 9 is in the hundredths place.
• 3 is in the thousandths place.
• 1 is in the ten thousandths place.

Numbers with no whole number part are often written with a zero in the ones place. This is done to make the decimal point easier to see. The zero is not required, however.

In .000049

• There are zeros in the tenths, hundredths, thousandths, and ten thousandths places.
• 4 is in the hundred thousandths place.
• 9 is in the millionths place.

No commas are used to help determine the groups on the right of the decimal point. This is because the first group has only 2 digits.

In 0.000000073

• There are zeros in the tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, and ten millionths places.
• 7 is in the hundred millionths place.
• 3 is in the billionths place.

To determine the place values for numbers with digits on both sides of the decimal point, start in the middle (at the decimal point) and work in both directions.

In 281.906

• 1 is in the ones place..
• 8 is in the tens place..
• 2 is in the hundreds place..
• 9 is in the tenths place..
• 0 is in the hundredths place..
• 6 is in the thousandths place..

In 58.0317

• 8 is in the ones place...
• 5 is in the tens place...
• 0 is in the tenths place...
• 3 is in the hundredths place...
• 1 is in the thousandths place...
• 7 is in the ten thousandths place...

Word Names

Word names are used to write or say numbers.

Whole Numbers

A three digit whole number is written with the hundreds digit spelled out, followed by the word hundred. If the tens digit is from 2 through 9, the appropriate tens word is next. These tens words end with ty, such as twenty and ninety. After the tens word, the ones digit is spelled out. However, if the tens digit is one, it is combined with the ones digit in a teen word, such as thirteen, or a variant such as eleven and twelve. If any of the digits is zero, nothing is written for it.

Examples

• 285 is written two hundred eighty five.
• The word name for 402 is four hundred two.
• The word name for 560 is five hundred sixty.
• The word name for 85 is eighty five.
• The word name for 417 is four hundred seventeen.
• The word name for 6 is six.
• The word name for 0 zero.

For larger whole numbers, the digits in each three digit group are written as they would be, if they were alone. This is followed by the group name. If an entire group is made up of zeros, nothing is written for it.

Examples

• 482,912 is written four hundred eighty two thousand, nine hundred twelve.
• The word name for 3,060,200 is three million, sixty thousand, two hundred.
• The word name for 14,700,000,000 is fourteen billion, seven hundred million..
• The word name for 811,001 is eight hundred eleven thousand, one..

Decimals

For decimal numbers, the digits to the right of the decimal point are written as if there were no decimal point. This is followed by the place value name of the furthest right digit. (These place values all end in ths.)

Examples

• 0.925 is written nine hundred twenty five thousandths.
• The word name for 0.30704 is thirty thousand, seven hundred four hundred-thousandths.
• The word name for 0.06 is six hundredths.
• The word name for 0.1 is one tenth.

Mixed Decimals

The word names for numbers with digits on both sides of the decimal point have four parts.

1. Write the digits on the left of the decimal point, as a whole number.
2. Write the word and to represent the decimal point.
3. Write the digits on the right of the decimal point, as a whole number.
4. Write the place value name of the furthest right digit.

The word and is only used to represent the decimal point; it is never used in the word name of a whole number.

Examples .

• 4.9 is written four and nine tenths.
• The word name for 267.158 is two hundred sixty seven and one hundred fifty eight thousandths.
• The word name for 3,000,000.000004 is 3million and 4 millionths.
• The word name for 12.9067 is twelve and 9 thousand sixty seven ten-thousandths.
• The word name for 5609.11 is five thousand,six hundred nine and eleven hundredt.hs