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Chapter 1: Problem 17

Give the place value of the 5 in each of the following numbers. $$267,894,335$$

Short Answer

Expert verified
The first '5' represents 5, and the second '5' represents 50,000.

Step by step solution

01

Identify the place occupied by each digit

Look at each digit in the number from right to left to determine its position. The number 267,894,335 has the following structure: - 5 at units (1's) place - 3 at tens (10's) place - 3 at hundreds (100's) place - 4 at thousands (1,000's) place - 9 at ten-thousands (10,000's) place - 8 at hundred-thousands (100,000's) place - 7 at millions (1,000,000's) place - 6 at ten-millions (10,000,000's) place - 2 at hundred-millions (100,000,000's) place
02

Locate the '5' in the number

In the number 267,894,335, identify each '5'. There are two '5's in this number, one located at the units place and another at the ten-thousands place.
03

Assign place values to each '5'

The first '5' from the right is in the units place. Thus, this '5' represents 5 ones = 5. The second '5' is in the ten-thousands place. Thus, this '5' represents 5 ten-thousands = 50,000.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Units Place
The units place, also known as the ones place, is the first digit to the right in any number without decimal points. It represents how many 'ones' are in the number. For instance, in the number 267,894,335, the last digit, which is 5, is located in this position.

In the units place:
  • The value of 5 is simply 5 times 1.
  • It signifies literally 5 one-dollar bills, or 5 groups of a single unit.
  • There are no other multiples involved, as it is the base of the number system.
This place holds much significance for counting and understanding the basic composition of any number.
Ten-Thousands Place
The ten-thousands place is several positions to the left from the units place. Specifically, it is the fifth digit from the right in a whole number. The number associated with this position represents how many groups of ten thousand are present.

For the number 267,894,335:
  • The digit 5 in the ten-thousands place translates to 5 groups of ten thousand.
  • This means the value of this 5 is calculated as 5 times 10,000 which equals 50,000.
  • This digit significantly affects the total value of the number due to its large multiplier.
By understanding the ten-thousands place, we recognize how even a single digit here can massively impact a number's overall value.
Digit Position
The position of a digit within a number determines its place value. This principle is fundamental in understanding how numbers are constructed and interpreted. Each digit in a number has different powers of ten based on its position, whether it's the unit, hundreds, or even million places.

In the example of 267,894,335:
  • The digit's exact location tells us how to compute its value.
  • Each move to the left increases the place value by a factor of ten.
  • This pattern underlies the entire base-10 numbering system used in everyday life.
Understanding digit position helps in grasping why numbers are arranged as they are, and how changing one digit's position can alter the entire number's value.

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