Example Question - floating-point notation
Here are examples of questions we've helped users solve.
Converting Large Number to Scientific and Floating-Point Notation
<p>To write the number "googol" in scientific notation, we recognize that a googol is defined as \(10^{100}\). Thus in scientific notation, it is simply:</p> <p>\(1 \times 10^{100}\)</p> <p>For the floating-point notation, which is typically used in calculators and computers for representing numbers, it would be impractical to display all the digits of a googol. However, depending on the calculator's display, it could be approximated to a certain number of significant digits. Since the options given are limited and none can fully represent a googol, there's no perfect match, but the understanding is that we're looking for the representation closest to \(10^{100}\).</p> <p>The closest approximation from the options for a floating-point notation is \(1 \times 10^{100}\), which aligns with the scientific notation.</p>
Converting Between Scientific Notation and Floating-Point Notation
<p>The mathematical concept requested in the image involves understanding and converting between scientific notation and floating-point notation. Typically, any number in scientific notation is written as \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.</p> <p>To convert from floating-point to scientific notation, we must adjust the decimal point to fit the criteria for \( a \), and then determine the appropriate exponent \( n \) that \( 10 \) must be raised to.</p> <p>Looking at the options provided:</p> <p>\( 20 \times 10^{-06} \) can be adjusted to \( 2.0 \times 10^{1} \times 10^{-06} = 2.0 \times 10^{-05} \)</p> <p>\( 0.02 \times 10^{-03} \) can be adjusted to \( 2.0 \times 10^{-02} \times 10^{-03} = 2.0 \times 10^{-05} \)</p> <p>\( 2 \times 10^{-05} \) is already in scientific notation.</p> <p>Without any additional context or numerical values in the image to match the options against, all three options provided are valid representations of numbers in scientific notation adjusted from the given floating-point notation starting points.</p>
Converting a Number to Scientific Notation and Floating-Point Notation
<p>For scientific notation, move the decimal point in 21.79 until there is one non-zero digit to the left of the decimal point:</p> <p>\(2.179 \times 10^1\)</p> <p>For floating-point notation, this is the same as the original number:</p> <p>\(21.79\)</p>
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