A whole number is any of the numbers 0, 1, 2, 3, .... Whole numbers are not negative, and do not have fractions or decimals.
Example: 0, 7, and 25 are whole numbers. -3 and 2.5 are not.
What is Place Value?
Place value tells you the value of each digit based on its position in the number.
For example, in 3,582:
3 is in the thousands place: 3 × 1,000 = 3,000
5 is in the hundreds place: 5 × 100 = 500
8 is in the tens place: 8 × 10 = 80
2 is in the ones place: 2 × 1 = 2
Example: In 4,105, the 1 is in the hundreds place, so it's worth 100.
What is a Fraction?
A fraction shows part of a whole. It is written as a/b, where a is the number of parts you have and b is the total number of equal parts.
Example: If you have a pizza cut into 8 slices and eat 3, you have 3/8 of the pizza left.
What is a Decimal?
A decimal is another way to show part of a whole, using a decimal point. For example, 0.5 means "five tenths," and is the same as the fraction 1/2.
Example:0.25 is the same as 1/4 (one quarter).
What is Absolute Value?
The absolute value of a number is its distance from zero on the number line. It is always positive or zero. For any number a, absolute value is written |a|.
Example:|7| = 7, |-7| = 7, |0| = 0
Is it correct to say "absolute value is to throw away the sign"? Almost! The absolute value is the distance from zero, so it is never negative. For positive numbers and zero, it stays the same. For negative numbers, it becomes positive. It's better to say: absolute value is the distance from zero, never negative.
What is Distance?
Distance is how far apart two numbers or points are. On a number line, the distance between a and b is |a - b| (the absolute value of their difference).
Example: The distance between 3 and 8 is |3 - 8| = 5.
Chapter 2: Examples & Exercises
Place Value
Example: In 6,382:
- 6 is in the thousands place (6 × 1000 = 6000)
- 3 is in the hundreds place (3 × 100 = 300)
- 8 is in the tens place (8 × 10 = 80)
- 2 is in the ones place (2 × 1 = 2)
Exercise 1: In the number 4,205, what is the value of 2?
Exercise 2: In 8,074, what is the place value of 7?