**Convert between standard and scientific notation :**

A number N is in scientific notation when it is expressed as the product of a decimal number between 1 and 10 and some integral power of 10.

N = a x 10ⁿ, where 1 ≤ a < 10 and n is an integer.

The steps for converting a number to scientific notation are as follows:

**Step 1 :**

Move the decimal point so that there is only one non-zero digit to its left.

**Step 2 :**

Count the number of digits between the old and new decimal point. This gives n, the power of 10.

**Step 3 :**

If the decimal is shifted to the left, the exponent n is positive. If the decimal is shifted to the right, the exponent n is negative.

Let us see some examples based on the above concept.

**Example 1 :**

Write the following numbers in scientific notation.

205852

**Solution :**

Since the given number is integer, we have to consider that the decimal point is in the last place.

Here n = 5 because the decimal point is shifted five places to the left .

**Example 2 :**

Write the following numbers in scientific notation.

3449098.96

**Solution :**

Now we are going to move the decimal point so that there is only one non-zero digit to its left.

**Here n = 6 because the decimal point is shifted five places to the left .**

**Example 3 :**

Write the following numbers in scientific notation.

0.00008035

**Solution :**

Now we are going to move the decimal point to the right so that there is only one non-zero digit to its left.

Since we are moving the decimal point to the right side, we have to put negative sign in the power.

Often, numbers in scientific notation need to be written in decimal form. To convert

scientific notation to integers we have to follow these steps.

**Step 1 : **

Write the decimal number.

**Step 2 : **

Move the decimal point the number of places specified by the power of ten to the right if positive, to the left if negative. Add zeros if necessary.

**Step 3 : **

Rewrite the number in decimal form.

Let us see some examples problems based on the above concept.

**Example 4 :**

Write the following numbers in decimal form.

5.236 x 10⁵

**Solution :**

Since we have positive number as power, we have to move the decimal point to the right side.

**Example 5 :**

Write the following numbers in decimal form.

6.415 x 10⁻⁶

**Solution :**

Since we have negative number as power, we have to move the decimal point to the left side.

We move 6 digits to the left side, we have to write zero for the remaining digits.

**Example 6 :**

Write the following numbers in decimal form.

1.72 x 10⁹

**Solution :**

We have positive number as power, we have to move the decimal point to the right side.

1.72 x 10⁹ = 1720000000

Since we have to move 9 digits to the right, we have to put zero for the remaining digits.

**Example 7 :**

How do you write 119,000 in scientific notation?

**Solution :**

Since the given number is integer, we have to consider that the decimal point is in the last place.

Now we are going to move the decimal point to the left side, so we have to put positive sign in the power.

**119000 = 1.19 x 10**⁵

**Example 8 :**

How do you write 7.2 × 10² in standard form?

**Solution :**

Since we have positive number in the power, we have to move the decimal point to the right side.

7.2 × 10² = 720

**Example 9 :**

How do you write 2,300 in scientific notation?

**Solution :**

Since the given number is integer, we have to consider that the decimal point is in the last place.

Now we are going to move the decimal point to the left side, so we have to put positive sign in the power.

**2300 = 2.3 x 10**³

**Example 10 :**

How do you write 38,000 in scientific notation?

**Solution :**

Since the given number is integer, we have to consider that the decimal point is in the last place.

Now we are going to move the decimal point to the left side, so we have to put positive sign in the power.

**38000 = 3.8 x 10**⁴

After having gone through the stuff given above, we hope that the students would have understood "Convert between standard and scientific notation".

Apart from the stuff given above, if you want to know more about "Convert between standard and scientific notation", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**