We’ll study about decimal exponents, square roots of a decimal, and logarithms with decimals, as well as how to add, subtract, multiply, and divide decimals. The subject isn’t very difficult: it all boils down to simple arithmetic, but we’ll take it slowly, so we don’t miss anything. We’ve divided the material below into parts for ease of reading, one for each operation possible in our decimal calculator.

What is decimal?

A decimal is a fraction that has been expressed in a certain way. For example, instead of writing 1/2, you may use the decimal 0.5 to represent the fraction, with the zero in the one’s place and the five in the tenth place. In algebra, a decimal number is defined as a number with a decimal point separating the entire number and fractional parts. A decimal point is a dot in a decimal number. The digits after the decimal point represent a number less than one.

Decimal derives from the Latin term Decimus, which means tenth, and is derived from the base word Decem, which means ten. As a result, the decimal system has a basis of 10 and is frequently referred to as a base-10 system. A number in the decimal system can also be referred to as decimal. When used as an adjective, decimal refers to a numerical system. The decimal point, for example, is the period in decimal numerals that divides one place from the tenth place.

The previous powers of ten are used to calculate decimals. As we progress from left to right, the place value of digits is divided by 10, resulting in tenths, hundredths, and thousandths being determined by the decimal place value. A tenth is equal to one-tenth of a tenth of a It is 0.1 in decimal form. The term “hundredth” refers to one-hundredth of a percent. It is 0.01 in decimal form.

Adding decimals calculator

The most crucial guideline to remember while adding decimals is to keep track of the decimal dot. As long as the two numbers have the same number of digits after the decimal dot, the operation reduces to doing the same thing we do when adding integers. If they don’t, we’ll make them. This situation implies that we may add as many zeros as we like after the last digit (but before the decimal dot) and still get the same number.

12.3 = 12.30 = 12.30000 = 12.300000

For example, if we wish to add two decimals, say 13.3 and 1.425, we first correct them such that the amount of digits after the dot is the same: 13.200 and 1.425. The sum may then be calculated using long addition:

13.200 + 1.1425 = 14.3425

Subtracting decimals calculator

Subtraction is essentially the same as addition. Sure, they’re the polar opposites of each other, but we can easily modify the subtraction to adding the number’s polar opposite. As a result, the two play under the same set of rules.

When subtracting decimals, the number of digits following the decimal dot must be the same in both expressions. If they don’t, we add a reasonable amount of zeros to the “shorter” number using the same approach we used in the “adding decimals calculator” section.

Multiplying decimals calculator

This one is a little unique. To begin with, multiplying decimals does not necessitate the same number of digits after the decimal dot in both expressions. Second, the result will have the same number of digits after the dot as the sum of the two numbers (see the addition and the subtraction sections for comparison). Aside from that, we use the same rules for long multiplication as we do for short multiplication.

Dividing decimals calculator

This one is unique. We don’t want to split decimals in some ways. Instead, we discover a quotient that is comparable but utilizes integers. We may multiply the dividend and divisor by any non-zero integer and still get the same value using the principles for simplifying fractions. We pick a number that is 10 to the power of the number of digits following the decimal dot in the number with the most of them. To put it another way, the multiplier is 1 plus as many zeros as the “longer” number has digits following the dot.

Decimal exponents

If we wish to elevate a decimal to an integer power, we do what we always do: multiply the number by the exponent’s value. Remember that you may multiply decimals using the methods from the multiplying decimals calculator section, or you can convert to ordinary fractions and multiply them that way.

When the decimal appears in the exponent, though, the tale becomes more fascinating. After that, we must consider it as a fractional exponent, as follows:

  • Make a simple fraction out of that (not a mixed number, mind you);
  • Raise the number to the power given by the numerator beneath the first exponent; and
  • Stake the root of the denominator

(Square) root of a decimal

Roots can be viewed as exponents, and the multiplicative inverse of the root order can be viewed as powers. This means, symbolically, that radicals obey the same laws as exponents when multiplying or dividing them. This is especially true for problems involving decimals.

\sqrt[b]{a}=a^{\frac{1}{b}}

When a decimal is contained within an integer-order root, we can either round up the result as we do with roots in general, or transform the number to a simple fraction and split the radical between the numerator and denominator. If, on the other hand, the decimal is in root order, we use the method above to convert it to an exponent and then follow the instructions from the previous section.

Logarithms with decimals

Logarithms are challenging in general. For example, the phrase logab informs us how much we need to increase a to get b. That appears to be a difficult question in and of itself, and we can make it much more difficult by adding decimals. The good news is that adding decimals to a logarithmic expression has little effect on the definition. Of course, various methods, such as changing the underlying formula, help us come closer to the desired result. In other words, if we have a logarithmic expression of a fraction (remember, decimals are fractions), we can extend it into the numerator’s log minus the denominator’s log.

Using the decimal calculator

Here are a few steps that can help you to simply use this calculator: 

 Choose the operation you want to do at the top of our tool. There are seven possibilities:

  • Select option that you need

Addition for the calculator that adds decimals;

Subtraction for the calculator that subtracts decimals;

Multiplication for the calculator for multiplying decimals;

For the dividing decimals calculator, divide;

Exponent for the calculator of decimal exponents;

For the decimal root calculator, use root;

Logarithms with decimals calculator, use Logarithm.

  • After you pick the procedure, a symbolic formula with the variables a and b appears beneath it.
  • Fill in the values for a and b in the formula’s appropriate fields. Integers, decimals, and other types of numbers can be used.
  • Underneath, you’ll find the answer.

Fraction to decimal conversion table

FractionDecimal
1/20.5
1/30.33333333
2/30.66666667
1/40.25
2/40.5
3/40.75
1/50.2
2/50.4
3/50.6
4/50.8
1/60.16666667
2/60.33333333
3/60.5
4/60.66666667
5/60.83333333
1/70.14285714
2/70.28571429
3/70.42857143
4/70.57142858
5/70.71428571
6/70.85714286
1/80.125
2/80.25
3/80.375
4/80.5
5/80.625
6/80.75
7/80.875
1/90.11111111
2/90.22222222
3/90.33333333
4/90.44444444
5/90.55555556
6/90.66666667
7/90.77777778
8/90.88888889
1/100.1
2/100.2
3/100.3
4/100.4
5/100.5
6/100.6
7/100.7
8/100.8
9/100.9
1/110.09090909
2/110.18181818
3/110.27272727
4/110.36363636
5/110.45454545
6/110.54545454
7/110.63636363
8/110.72727272
9/110.81818181
10/110.90909091

FAQ

What is a terminating decimal?

As the name implies, a terminating decimal is a decimal with an end. For example, 1 / 4 can be written as 0.25 as a terminating decimal. 1 / 3 cannot, on the other hand, be written as a terminating decimal since it is a recurring decimal that continues indefinitely.

Are decimals integers?

Integers, like whole numbers, do not include fractions or decimals.

How do I multiply decimals without a calculator?

To multiply decimals, start by multiplying as if there isn’t one. Then, for each component, count the number of digits following the decimal. Finally, insert the same amount of digits after the decimal in the product.

How do I calculate decimal exponents?

When multiplying decimals, count the number of decimal places in the base number first, just as you would when multiplying decimals (see Decimal Multiplication). Then increase the result by the exponent. The total number of decimal places in the solution will be this.

How to convert decimal to percent?

To get a percentage, multiply a decimal by 100 (just move the decimal point 2 places to the right). For example, 0.065 percent is 6.5 percent, and 3.75 percent equals 375 percent. Simply multiply to determine a percentage of a number, such as 30% of 40.

How to convert percent to decimal?

Divide a percentage by 100 to convert it to a decimal. As a result, 25% is 25/100, or 0.25. To get a percentage, multiply a decimal by 100 (just move the decimal point 2 places to the right).