# Place Value

### What is an example of place value?

#### A

Place value is a convenient way of separating the value of each digit in a number. An example of place value can be seen when working with money. For example, $$45.86$$ consists of digits in the tens, ones, tenths, and hundredths place. When this value is split apart according to its place value, the amount becomes $$40+5+\frac{8}{10}+\frac{6}{100}$$. Place value is based on the base ten number system which is why digits increase or decrease by a factor of ten.

### What are tens and ones?

#### A

Tens and ones are represented by the first two digits to the left of the decimal point. For example, in the value $$94.0$$, the $$4$$ represents $$4$$ groups of one $$(4)$$, and the $$9$$ represents $$9$$ groups of $$10$$ $$(90)$$. When $$4$$ ones and $$9$$ tens are combined, the total value becomes $$90+4=94$$.

### What is the ones place in a decimal?

#### A

The ones place is the digit that is directly to the left of the decimal point. For example, in the value $$3.4$$, the digit $$3$$ is in the ones place. In a number with no decimal point, the ones place is the digit farthest to the right. For example, in the value $$459$$, the $$9$$ is in the ones place because $$459$$ is essentially $$459.0$$.

### Why is there no oneths place?

#### A

There is not a “oneths” place because digits to the right of the decimal point become smaller by a factor of ten. This means that moving from the ones place to the tenths place is the result of dividing $$1$$ by $$10$$, which is one-tenth, not one-oneth.

### Which place is the tenths place?

#### A

In a decimal value, the first digit to the right of the decimal point is in the tenths place. For example, in the value $$34.592$$, the digit $$5$$ is in the tenths place. This $$5$$ represents five tenths, or $$\frac{5}{10}$$.

### What is the definition of a tenth?

#### A

A tenth represents the fraction “out of ten”. In a decimal value like $$3.4$$, this means three ones, and $$4$$ tenths. Another way to look at $$3.4$$ is $$\frac{3}{1}+\frac{4}{10}$$. The tenths place is always the digit directly to the right of the decimal point.

### Where is the tens place in a number?

#### A

The tens place is always located two digits to the left of the decimal point. Remember, even whole numbers can be written with a decimal point. For example, $$34$$ can be written as $$34.0$$, which means that $$3$$ is in the tens place. This $$3$$ represents $$3$$ groups of ten. In the decimal value $$198.478$$, the second digit to the left of the decimal is $$9$$. This means that the $$9$$ represents $$9$$ groups of $$10$$, or $$90$$.

### How many tens make a thousand?

#### A

The base ten number system is convenient because all digits moving to the left become $$10$$ times as large, and all digits moving to the right become $$10$$ times smaller. This means that all place values can be compared by a factor of ten. For example, tens are $$10$$ times as large as ones. Hundreds are $$10$$ times as large as tens. Thousands are 10 times as large as hundreds. When making the jump from tens to thousands, we would need to multiply by $$10$$ twice. So it would take $$100$$ tens to make a thousand. For example, $$1{,}000$$ is $$100$$ times as large as $$10$$.

## Practice Questions

Question #1:

What is 7,645 written in expanded form?

$$7+6+4+5$$
$$76+45$$
$$7,000+600+40+5$$
$$700+64+5$$

The correct answer is $$7,000+600+40+5$$. To write a number in expanded form, write an addition problem that adds the value of each number. 7 is in the thousands place, so it represents 7,000. 6 is in the hundreds place, so it represents 600. 4 is in the tens place, so it represents 40. And 5 is in the ones place, so it represents 5. Added together this looks like: $$7,000+600+40+5$$.

Question #2:

What is the place value of 9 in 293.76?

Hundredths

Tenths

Tens

Hundreds

The correct answer is Tens. Place value names can be determined by their position in respect to the decimal point. The position to the left of the decimal point is the ones place. To the left of that is the tens place, and to the left of that is the hundreds place. The position to the right of the decimal point is the tenths place, and the one to the right of that is the hundredths place. Therefore, 9 is in the tens place.

Question #3:

What is 12,643.57 in expanded form?

$$10,000+2,000+600+40+3+\frac{5}{10}+\frac{7}{100}$$
$$12,000+643+\frac{57}{100}$$
$$12,000+600+43+\frac{57}{100}$$
$$12,643+\frac{57}{100}$$

The correct answer is $$10,000+2,000+600+40+3+\frac{5}{10}+\frac{7}{100}$$. To write a number in expanded form, write an addition problem that adds the value of each number. 1 is in the ten-thousands place, so it represents 10,000. 2 is in the thousands place, so it represents 2,000. 6 is in the hundreds place, so it represents 600. 4 is in the tens place, so it represents 40. 3 is in the ones place, so it represents 3. 5 is in the tenths place, so it represents $$\frac{5}{10}$$. And 7 is in the hundredths place, so it represents $$\frac{7}{100}$$. Added together this looks like: $$10,000+2,000+600+40+3+\frac{5}{10}+\frac{7}{100}$$

Question #4:

What is the place value of 3 in 192.36?

Tens

Ones

Tenths

Hundredths

The correct answer is Tenths. Place value names can be determined by their position in respect to the decimal point. The position to the left of the decimal point is the ones place. To the left of that is the tens place, and to the left of that is the hundreds place. The position to the right of the decimal point is the tenths place, and the one to the right of that is the hundredths place. Therefore, 3 is in the tenths place.

Question #5:

What is the place value of 6 in 162,497,132.498?

Ten-millions

Millions

Hundred-thousands

Ten-thousandths