What is standard form in math? What does a number in standard index form mean? The English word “standard” has the thought of being the required level of quality. Does this definition mean that numbers not in “standard form” are not quality numbers? Not at all. Then when do we say a number is written in standard form? And how do we write numbers in standard form?

Let’s first look at why we say certain numbers are in standard form or standard index form. It is a system agreed upon by mathematicians to write numbers which are very large or very small. Since it was generally accepted, the term “standard” was used. So it has nothing to do with the quality of a number. It must be noted however that in the USA, a number in standard form is referred to as the scientific notation..

The standard form in math is also called the standard index form and calling it the standard index form sheds more light on what it is really about. Indices deal with powers of numbers. In standard form, powers of 10 are used to express how large or small a number is. So if any number, which is equal to or greater than 1 but less than 10, is multiplied by 10 raised to a certain power, it is said to be in standard form.

Mathematically, any number in the form “a x 10b where 1 ≤ a < 10 and b is any positive or negative whole number, is said to be in standard form or standard index form.

So the following numbers are said to be in standard form in math:

2 x 10 12 Reason: This is because 2 is greater than 1 and the power of 12 is a positive whole number

Reason: This is because 2 is greater than 1 and the power of 12 is a positive whole number 9.9 x 10 -20 Reason: This is because 9.9 is greater than 1 and the power of -20 is a negative whole number.

Reason: This is because 9.9 is greater than 1 and the power of -20 is a negative whole number. 1 x 10-5 Reason: This is because 1 is equal to 1 and the power of -5 is a negative whole number.

The following numbers are not in standard form even though they look like that:

0.1 x 10 12 Reason: 0.1 is not equal to or greater than one.

Reason: 0.1 is not equal to or greater than one. 10 x 10 -5 Reason: 10 is not less than 10.

Reason: 10 is not less than 10. 19.9 x 10-20 Reason: 19.9 is not less than 10.

What a Positive Power Mean

If a number is written in standard form then a positive power of 10 means that the number is 10 or greater than 10. Multiplying a number by 10b , where b is a positive integer, is just moving the decimal point to the right, “b” number of times.

So for eaxample, what 1 x 105 actually mean is multiply 1 by 10 x 10 x 10 x 10 x 10. Since one is a whole number the decimal point is on it’s right. We just have to move it 5 times to the right. We put zero before each move since there is nothing to the right of it. So 1 x 105 in full will be 100000.

Similarly, to write 2.5 x 105 in full we will have to multiply 2.5 by 10 x 10 x 10 x 10 x 10. This time we have a decimal number so we just move the decimal point 5 points to the right. This gives 250 000. We put zero where there is no number.

So multiplying by a positive power of 10 makes the number large. So the bigger the power of 10 gets the bigger the number becomes.

What a negative power mean

For a number written in standard form a negative power of 10 means that the number is less than one. Multiplying a number by 10b , where b is a negative integer, is just moving the decimal point to the left, “b” number of times.

For example if we have 2.4 x 10-4 , it means we will have to multiply 2.4 by 10-1 x 10-1 x 10-1 x 10-1 . Whenever we multiply by 10-1 we move the decimal point to the left. So if we multiply by 10-4 , it means we will have to move the decimal point to the left, 4 times. So 2.4 x 10-4 in full will be 0.00024.

Now note that, multiplying by a negative power of 10 always makes the number smaller. The higher the absolute value of the negative power the smaller the number.

What a power of zero mean

Also for a number written in standard form a power of zero means that the number is 1 or greater than 1 but less than 10. This is true because 100=1 and for a number to be in standard form the non exponent part should be 1 or greater than one but less than 10. Since any number multiplied by 1 is itself we can confidently say that a standard form number with power of zero should be 1 or greater than 1 but less than 10.

So multiplying by a 10 with power of zero means that the number stays the same

For example, 2.5 x 100 = 2.5 x 1 = 2.5

How to change a number to Standard Form in math

Now that we know what a number in standard form really is, we will now look at how to put a number in standard form. Before you change a number to standard form these are some things to keep in mind.

Things to note in changing a number to Standard form in math

A number which is greater than 1 must have a positive power of 10 in standard form

A number which is less than 1 must have a negative power of 10 in standard form

Procedure:

Step 1: Given any number, move the decimal place to between the first and second significant figures from the left of the number.

Changing to standard form in math. Example 1:

234 becomes 2.34

23.4 becomes 2.34

46788.01 becomes 4.678801

0.00034 becomes 3.4

0.021 becomes 2.1

Step 2: Count the number of times you moved the decimal point to get it in between the two significant numbers. Also take note of the direction in which the decimal point was moved. ie. either to the left or to the right.

Examples 2

For 234 to become 2.34 we moved the decimal point 2 places to the left.

And for 46788.01 to become 4.678801, we moved the decimal point 4 places to the left.

Also for 0.00034 to become 3.4, we moved the decimal point 4 places to the right.

Furthermore for 0.021 to become 2.1, we moved the decimal point 2 places to the right.

Step 3: If in step 2, you moved the decimal point to the right it means you will have a negative power of 10 in standard form but if you moved the decimal point to the left it means that when written in standard form you will a positive power of 10. The number of times you moved the decimal place in step 2 will be the value of the power of 10 in standard form.

Let’s use the following examples to further enhance our understanding of the steps involved.

Question 1: Write 234 in standard index form.

Answer: 2.34 x 102

Reason: The decimal point was moved 2 places to the left to get 234 to become 2.34. Since it was moved to the left we know that in standard form the power of 10 will be positive. Since the decimal point was moved 2 times, we have positive 2 to be the power of 10.

Question 2: Write 46788.01 in standard form

Answer: 4.678801 x 104

Reason: The decimal point was moved 4 places to the left to get 4.678801. Since it was moved to the left we know that in standard form the power of 10 will be positive. That is why the final answer is 4.678801 x 104.

Question 3: Write 0.00034 in standard form

Answer: 3.4 x 10-4

Reason: The decimal point was moved 4 places to the right. Since it was moved to the right we know that in standard form the power of 10 will be negative. So final answer is 3.4 x 10-4.

Question: Write 0.02001 in standard index form.

Answer: 2.001 x 10-2

Reason: To get the decimal point in between the first two significant numbers, we move it two places to the right to get 2.001. Since it was moved to the right we know that in standard form the power of 10 will be negative. So final answer is 2.001 x 10-2

Standard Form in math. Conclusion:

I’m sure by now, you know how easy it is to convert a number to the standard index form. Share the word. Do Justice to math and love math

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