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### MEAP Preparation - Grade 7 Mathematics1.151 Scientific Notation for Natural Numbers

1. Scientific notation is used to express very large or very small numbers.
2. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10.
Co-efficient x BaseExponent

• The coefficient must be greater than or equal to 1 and less than 10.
That is 1 <= 1 < 10
• The base must be 10.
• The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.
A negative exponent means that the decimal is moved to the left when changing to standard notation.
• Example:
3.14 x 1015 is correct scientific notation
31.4 x 1014 is not correct scientific notation

To change Natural Number to Scientific Notation:

1. Place decimal point such that there is one non-zero digit to the left of the decimal point.
2. Count number of decimal places the decimal has "moved" from the original number. This will be the exponent of the 10.
3. The original number here is greater than 1, the exponent is positive (If the original number was less than 1, the exponent is negative)

Examples:
The number 4,000,000,000 can be written in scientific notation as 4x109.
The number 1 can be written in many ways 0.1x101, 1.0x100 etc. But the scientific notation is expressed as 1x100. Since the number is always 1 or more and less than 10.

 Standard Number Scientific Notation 1 1.0 x 100 5 5 x 100 8 8.0 x 100 10 1.0 x 101 15 1.5 x 101 25 2.5 x 101 35 3.5 x 101 100 1.0 x 102 200 2.0 x 102
 Standard Number Scientific Notation 210 2.1 x 102 1000 1.0 x 103 1020 1.02 x 103 123,000,000 1.23 x 108 456,000 4.56 x 105 1,000,000 1.0 x 106 1,000,000,000 1.0 x 109 1,000,000,000,000 1.0 x 1012 123,000,000,000 1.23 x 1011

Directions: Choose the scientific notation for the numbers given below. Also write atleast 5 examples of your own.
 Q 1: 1,000,000,000,0001.0 x 10111.0 x 10121.0 x 1010 Q 2: 10001.0 x 1021.0 x 1011.0 x 103 Q 3: 1001.0 x 1031.0 x 1021.0 x 101 Q 4: 292.9 x 10129 x 101.29 x 101 Q 5: 10100 x 10110 x 1011.0 x 101 Q 6: 770 x 100.7 x 1007.0 x 100 Q 7: 11110 x 1011.1 x 10111 x 101 Q 8: 234,000,0002.34 x 1072.34 x 1082.34 x 106 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!