and this one too please i'm horrible with exponents.
Express .0370700 in exponential form, using standard scientific or "e" notation (for example, 105 = 1.05e2). Enter the correct number of significant figures.
Express .0370700 in exponential form, using standard scientific or "e" notation (for example, 105 = 1.05e2). Enter the correct number of significant figures.
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It's 5.981025e9 (and the other one is 3.707e-2).
Scientific form is a way of representing a number by two numbers: the mantissa and exponent (mantissa before the e, exponent after) - to get back to the real value, you multiply the mantissa by 10^exponent (10 to the power of the exponent, or multiply by 10 exponent-times). For a number to be scientific form, the mantissa must be a between 1 and 10 (unless the number is 0 - but otherwise ignore this). So you effectively just move the decimal point so that the number becomes a number between 1 and 9; then, the exponent is how many places you moved it.
So for example, with 5,981,025,000, for the mantissa to be between 1 and 10 we must move the decimal place to just after the 5. (It will always be after the first non-zero number (unless the whole number is 0)). We had to move the decimal point 9 places to the left, so to get from 5.981025 to 5,981,025,000 we must move the decimal point 9 places to the right: this means that the exponent is +9 - we must multiply the mantissa by 10 nine times to get the original number. i.e. the answer is 5.981025e9.
Similarly with the other one, we move the decimal point to just after the 3 to get the mantissa; to get back to the original number we must then divide by 10^2 (divide by 10 twice), so the exponent is -2 (same as multiplying by 1/100 or 10^-2). So this answer is 3.707e-2.
You do not need significant figures... scientific notation doesn't necessarily involve rounding the number.
Hope that helped.
Scientific form is a way of representing a number by two numbers: the mantissa and exponent (mantissa before the e, exponent after) - to get back to the real value, you multiply the mantissa by 10^exponent (10 to the power of the exponent, or multiply by 10 exponent-times). For a number to be scientific form, the mantissa must be a between 1 and 10 (unless the number is 0 - but otherwise ignore this). So you effectively just move the decimal point so that the number becomes a number between 1 and 9; then, the exponent is how many places you moved it.
So for example, with 5,981,025,000, for the mantissa to be between 1 and 10 we must move the decimal place to just after the 5. (It will always be after the first non-zero number (unless the whole number is 0)). We had to move the decimal point 9 places to the left, so to get from 5.981025 to 5,981,025,000 we must move the decimal point 9 places to the right: this means that the exponent is +9 - we must multiply the mantissa by 10 nine times to get the original number. i.e. the answer is 5.981025e9.
Similarly with the other one, we move the decimal point to just after the 3 to get the mantissa; to get back to the original number we must then divide by 10^2 (divide by 10 twice), so the exponent is -2 (same as multiplying by 1/100 or 10^-2). So this answer is 3.707e-2.
You do not need significant figures... scientific notation doesn't necessarily involve rounding the number.
Hope that helped.
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before we answer we need to know how many significant figures u need
2 sig: 6.0e9 & 3.7e-1
3: 5.98e9 & 3.71e-2
etc.
2 sig: 6.0e9 & 3.7e-1
3: 5.98e9 & 3.71e-2
etc.