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Numbers in standard form, also known as scientific notation, are expressed as a×10n, where 1≤|a|<10 and n is an integer. This notation is particularly useful when dealing with very large or very small numbers, as it allows for a concise representation.
When performing operations with numbers in standard form, it is crucial to follow the rules of arithmetic carefully. Here are some examples to illustrate the operations:
Addition:
When adding numbers in standard form, it is essential to have the same exponent. If the exponents are different, adjust them appropriately before performing the addition.
(3×104)+(5×103)=(3×104)+(0.5×104)=3.5×104
Subtraction:
Similar to addition, when subtracting numbers in standard form, ensure that the exponents are the same before performing the subtraction.
(7×106)−(2×105)=(7×106)−(0.02×106)=6.98×106
Multiplication:
When multiplying numbers in standard form, multiply the coefficients (the numbers in front of the power of 10) and then add the exponents of the powers of 10.
(12×103)×(4×105)=48×108Remember to always express your final answer in standard form, ensuring that the coefficient is a number between 1 and 10 (including 1 but excluding 10). Adjust the power of 10 to compensate any changes you have made to the coefficient.
=4.8×109Division:
For division, divide the coefficients and then subtract the exponent in the denominator from the exponent in the numerator.
3×1096×102=0.5×107
Again remember to always express your final answer in standard form, ensuring that the coefficient is a number between 1 and 10 (including 1 but excluding 10). Adjust the power of 10 to compensate any changes you have made to the coefficient.
=5×106This video on Scientific Notation is from Revision Village and is aimed at students taking the IB Maths Standard level course.
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