#POWER OF TEN MATH DOWNLOAD#

If you think the POWERS_OF_TEN array literal initialiser is ugly (I agree), there is a shorter and possibly less error-prone way: private static final long POWERS_OF_TEN = IntStream. So #2 array lookup is the fastest, confirming the accepted answer is correct. PowerOfTenBenchmark.switchLookup thrpt 15 461.318 ± 4.941 ops/us PowerOfTenBenchmark.arrayLookup thrpt 15 515.684 ± 10.056 ops/us PowerOfTenBenchmark.mathPow thrpt 15 24.134 ± 32.132 ops/us Therefore we have developed the educational program 'Powers of Ten'. Here is the JMH benchmark code: private static final long POWERS_OF_TEN = Īnd (drumroll.) here are the results: Benchmark Mode Cnt Score Error Units Powers of ten is an item of algebra that causes sometimes problems for the math students of high schools.

Look up in a hard-coded switch statement.

Look up in an array, as per the accepted answer.

I tested the performance of three approaches using JMH: Problem and check your answer with the step-by-step explanations.This question is quite old, but for people landing here from a search, I hope this is useful.

Try the given examples, or type in your own Problem solver below to practice various math topics.

#POWER OF TEN MATH DOWNLOAD#

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics. Then Elena said, “In four years, I’ll be as old as Katie is now!” If Elena is currently e years old and Katie is k years old, which system of equations matches the story? Elena noticed that, nine years ago, her cousin Katie was twice as old as Elena was then.Why might exponential notation be preferable to answer these questions? Hence, the 10 power in long-form is the number 1 followed by n zeroes where n is the number that is greater than 0. In other words, the power of 10 states that the 10 multiplied to itself n number of times (when the power is any positive integer). Write an expression for the number of amoebas after 24 hours.Į. In Mathematics, the power of 10 is any whole-valued (integer) power of the number 10. Write an expression for the number of amoebas after 6 hours.ĭ. How many amoebas are there after 2 hours?Ĭ. How many amoebas are there after 1 hour?ī. Every hour, each amoeba divides to form two more.Ī. One hour later, each of the two amoebas divides to form two more. Ask the students to use the internet to find scenarios where the powers of ten appear in the real world. Have students complete the sort before filling in the Powers of Ten Chart. An amoeba divides to form two amoebas after one hour. Strategies for Differentiation Create a sort including powers of ten, expanded forms, and products.If you layered the cubes to make one big cube, what would be the dimensions of the big cube? Explain your reasoning. If you arranged the cubes on the floor to make a square, would the square fit in your classroom? What would its dimensions be? Explain your reasoning.Ĭ. If you stacked the cubes on top of one another to make an enormous tower, how high would they reach? Explain your reasoning.ī. You have 1,000,000 number cubes, each measuring one inch on a side.Ī.

Write each expression with a single exponent:.

Again the base number is 10 but now 3 is the exponent it equals 10 x 10 x 10 The third power ten is 1000. Verse 1 The base number is 10 2 is the exponent 10 to the second means 10 x 10 This power of ten is 100. How many other whole numbers can you raise to a power and get 4,096? Explain or show your reasoning. To find a power of ten Look at the exponent Take your pencil and then Multiply that many tens. Elena says, “10 2 is multiplied by itself 3 times, so 10 2 ĭo you agree with either of them? Explain your reasoning.Ģ 12 = 4,096.Andre says, “When you multiply powers with the same base, it just means you add the exponents, so 10 2.How many cubic meters of oil is this? Do you think this would be enough to fill a pond, a lake, or an ocean? If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures 10 3 meters on each side.Use the patterns you found in the table to rewrite (10 m) n as an equivalent expression with a single exponent, like 10 x. To divide powers of 10, subtract the exponents that is, subtract the exponent of the second number (the divisor) from the exponent of the first number (the.If you chose to skip one entry in the table, which entry did you skip? Why? You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.ī. Complete the table to explore patterns in the exponents when raising a power of 10 to a power. To multiply a whole number by a power of ten, add the same number of zeros to the end of the number as the power of ten.

Power of ten math