1.1 Introduction to whole numbers  (Page 2/13)

Find the total value of each kind of bill, and then add to find the total. The wallet contains $\text{\$374}.$

Base-10 blocks provide another way to model place value, as shown in [link] . The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of $10$ ones, and the hundreds square is made of $10$ tens, or $100$ ones.

[link] shows the number $138$ modeled with $\text{base-10}$ blocks.

Use place value notation to find the value of the number modeled by the $\text{base-10}$ blocks shown.

Solution

There are $2$ hundreds squares, which is $200.$

There is $1$ tens rod, which is $10.$

There are $5$ ones blocks, which is $5.$

Digit	Place value	Number	Value	Total value
$2$	hundreds	$2$	$100$	$200$
$1$	tens	$1$	$10$	$10$
$5$	ones	$5$	$1$	$+5$
				$215$

The $\text{base-10}$ blocks model the number $215.$

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Use place value notation to find the value of the number modeled by the $\text{base-10}$ blocks shown.

176

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Use place value notation to find the value of the number modeled by the $\text{base-10}$ blocks shown.

237

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Identify the place value of a digit

By looking at money and $\text{base-10}$ blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called periods. The periods are ones, thousands, millions, billions, trillions , and so on. In a written number, commas separate the periods.

Just as with the $\text{base-10}$ blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is ten times the value of the place to the right of it.

[link] shows how the number $\mathrm{5,278,194}$ is written in a place value chart.

• The digit $5$ is in the millions place. Its value is $\mathrm{5,000,000}.$
• The digit $2$ is in the hundred thousands place. Its value is $\mathrm{200,000}.$
• The digit $7$ is in the ten thousands place. Its value is $\mathrm{70,000}.$
• The digit $8$ is in the thousands place. Its value is $\mathrm{8,000}.$
• The digit $1$ is in the hundreds place. Its value is $100.$
• The digit $9$ is in the tens place. Its value is $90.$
• The digit $4$ is in the ones place. Its value is $4.$

Use place value to name whole numbers

When you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period followed by the name of the period without the ‘s’ at the end. Start with the digit at the left, which has the largest place value. The commas separate the periods, so wherever there is a comma in the number, write a comma between the words. The ones period, which has the smallest place value, is not named.