Place Value: What Are Decimals?

What are decimals? Decimals are a way of representing fractions using powers of 10. A decimal is a number that has a decimal point in it. The decimal point separates the whole numbers from the fractional part of the number. Decimals are used in many everyday situations. For example, when we calculate how much change to give someone, or how much we should tip in a restaurant. We also use decimals when we measure things like length, weight, or capacity. In this article, we will explore what decimals are and how to use them. We will also look at some examples of where decimals are used in everyday life.

What is Place Value?

In mathematics, place value is the value of a digit based on its position in a number. Place value is a key concept in understanding decimals.

The place value of a digit depends on its position in the number. The place value of the digits in the number 1234567890 can be seen in the following table:

Digit 1 2 3 4 5 6 7 8 9 0
Position ones, tens, hundreds, etc. . . . . . . ten millions
Place Value 1 x 10^0 = 1 ones 2 x 10^1 = 20 tens 3 x 10^2 = 300 hundreds
4 x 10^3 = 4000 thousands 5 x 10^4 = 50000 ten thousands 6 x 10^5 = 600000 one hundred thousands 7 x 10^6 = 7000000 one million 8 x 10^7 = 80000000 ten millions 9 x 10^8 = 900000000 one hundred millions 0 x 10^9= 0 one billion
As can be seen from the table, each digit has a place value that is a power of ten. The zero has a place value of zero because it doesn’t change the value of any other digit that comes after it. For example, in the number 1230405000, the 4 means 4 ones (4×10^0), but because there is a

What are Decimals?

Decimals are numbers that are less than one or greater than one. They are written using a decimal point. For example, 0.1, 0.01, and 0.001 are all decimals.

Decimals can be used to represent fractions. For example, if we want to represent the fraction 1/10 as a decimal, we can write it as 0.1. Similarly, if we want to represent the fraction 1/100 as a decimal, we can write it as 0.01.

Decimals can also be used to represent numbers that are not whole numbers. For example, if we want to represent the number 1.5 as a decimal, we can write it as 1.5.

Decimals can be written in expanded form using place value notation . For example, the decimal 0.1 can be written as 1 x 10-1 . This is read as “one times ten to the negative first power”. Similarly, the decimal 0.01 can be written as 1 x 10-2 . This is read as “one times ten to the negative second power”.

Place Value of Decimals

Decimals are numbers that have a fractional component, which expresses the number’s value relative to one. In other words, decimals are numbers that represent a division of something whole. For example, the decimal 0.5 represents one-half, or 50%.

The place value of decimals is based on the position of the decimal point. The decimal point separates the whole number part of a decimal from the fractional part. The place value of each digit to the left of the decimal point is ten times greater than the place value of each digit to the right of the decimal point.

For example, in the decimal 0.5, the 5 is in the ones place and has a place value of 5. The 0 is in the tenths place and has a place value of 0.1, or 1/10. To find an equivalent fraction for 0.5, we can multiply both sides by 10:

0.5 * 10 = 5

Therefore, 0.5 is equivalent to 5/10, or one-half.

Rounding Decimals

When we round decimals, we look at the number to the right of the decimal point. If this number is less than 5, we don’t change the decimal number. If the number is 5 or greater, we add 1 to the decimal number. For example, if we round 3.14, we would leave it as 3.1 since 4 is less than 5. But if we round 3.15, we would change it to 3.2 since 5 is greater than or equal to 5.

Operations with Decimals

Decimals are numbers that are used to represent a fraction of something. For example, when we say that there are “5.4” hours in a day, we are using a decimal to represent a fraction of an hour. Decimals can be used to represent any number, no matter how small or large.

Decimals are written using a decimal point. The decimal point is used to separate the whole number part of a decimal from the fractional part. In the example above, the 5 is the whole number part and the 4 is the fractional part. The fractional part is always written after the decimal point.

When we add or subtract decimals, we line them up on either side of the decimal point and then add or subtract as usual. For example:

2.1 + 3.4 =

5.5 – 1.2 =

4.7 + 6.9 =

11.6 – 2.3 =

When we multiply decimals, we again line them up on either side of the decimal point and then multiply as usual:

2 x 3 =
6 x 4 =
0.7 x 0.9=

Conclusion

Decimals are a way of representing numbers that are not whole numbers. They are used when we need to be more precise in our measurements, such as when measuring length or weight. Decimals are written using a decimal point, which separates the whole number part of the number from the decimal part. The decimal point can be placed anywhere in the number, but is typically placed after the first digit to the right of the zero.