Khan/khan-exercises

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 Understanding moving the decimal
randRangeNonZero( -1, 1 ) ( PM === 1 ? "multiply" : "divide" ) randRange( 0, 99999 )
randRange( 1, 5 ) randRange( 1, 5 )
A / pow( 10, A_DECIMAL ) A / pow( 10, B_DECIMAL ) ( PM === 1 ? ( A_DECIMAL - B_DECIMAL ) : ( B_DECIMAL - A_DECIMAL ) )

How many times do you need to OPERATOR A_FLOAT.toFixed( A_DECIMAL ) by ten to get B_FLOAT.toFixed( B_DECIMAL )?

POW_DIFF

init({ range: [ [ -1, 11 ], [ -1, 3 ] ], scale: [30, 45] }); var digitsA = KhanUtil.digits( A ); //Pad zeroes if need be for the decimal point while ( digitsA.length < A_DECIMAL + 1) { digitsA.push( 0 ); } var digitsB = digitsA.slice(); //For the leading zero 0.# only occurs with division if ( digitsA.length < B_DECIMAL + 1) { digitsA.push( ' ' ); digitsB.push( 0 ); } drawDigits( digitsA.reverse(), 0, 1); drawDigits( digitsB.reverse(), 0, 0); for ( var i = 0; i < POW_DIFF; i++) { if ( PM === 1 ) { arc( [ digitsA.length - A_DECIMAL + i, 1.5 ], 0.5, 0, 180, { stroke: "blue" } ); label( [ digitsA.length - A_DECIMAL + i, 2 ], i+1, "above" ); if ( i === POW_DIFF - 1 ) { //hack for the final arrow...is there a better way? line( [ digitsA.length - A_DECIMAL + i + 0.5, 1.5 ], [ digitsA.length - A_DECIMAL + i + 0.5, 1.46 ], { stroke: "blue", arrows: "->" } ); } } else { //to draw the final arrow if ( i === POW_DIFF - 1 ) { style({ arrows: "->" }); } arc( [ digitsA.length - A_DECIMAL - (i + 1), 1.5 ], 0.5, 0, 180, { stroke: "blue" } ); label( [ digitsA.length - A_DECIMAL - (i + 1), 2 ], i+1, "above" ); } } //draw a black ellipse to be used as a decimal point style({ fill: "#000" }); ellipse( [ digitsA.length - A_DECIMAL - 0.5, 0.8 ], [ 0.09, 0.06 ] ); ellipse( [ digitsB.length - B_DECIMAL - 0.5, -0.2 ], [ 0.09, 0.06 ] ); var labelstr = "\\text{The decimal point needs to be moved " + POW_DIFF + " time" + ( POW_DIFF !== 1 ? "s.}" : ".}"); label ([ digitsA.length + 0.5, 0.5 ], labelstr, "right", 1);

Moving the decimal one position to the PM === 1 ? "right" : "left" is the same as PM === 1 ? "multiplying" : "dividing" by ten once.

Thus, moving the decimal right POW_DIFF times is the same as multiplying by ten POW_DIFF times, or multiplying by pow( 10, POW_DIFF ):

{A_FLOAT.toFixed( A_DECIMAL )} * {pow( 10, POW_DIFF )} = {B_FLOAT.toFixed( B_DECIMAL )}

Thus, moving the decimal left POW_DIFF times is the same as dividing by ten POW_DIFF times, or dividing by pow( 10, POW_DIFF ):

{A_FLOAT.toFixed( A_DECIMAL )} \div {pow( 10, POW_DIFF )} = {B_FLOAT.toFixed( B_DECIMAL )}

You need to OPERATOR by ten POW_DIFF times.

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