桁 and 桁違い: digit positions and a striking difference
Distinguish a digit-position error in an amount from a striking difference in a record, without assigning a fixed multiplier to 桁違い.
Positions in an amount
桁, read けた, refers to a digit position or the number of digits. 合計金額の桁を一つ間違えて入力した。 reports entering the total amount with a one-position error.
千円と一万円では金額が違います。 says that one thousand and ten thousand yen are different amounts. Check digit positions and zeros when copying an amount.
An assessment of a large difference
桁違い, read けたちがい, can indicate a difference in digit positions or a striking difference in scale. 優勝者の記録は他の選手と桁違いだった。 assesses the winner’s record as markedly different from the others.
That assessment alone does not establish a factor of exactly ten. The type of record and the actual values are needed for a numerical comparison.
An error or an assessment
見積書の数字が桁違いなので、入力ミスを疑った。 says that an input error was suspected because of a digit-position discrepancy in the quotation. Suspicion differs from confirmation.
Compare the original amount when checking entry, and compare the stated values when assessing records. Do not assign the same fixed multiplier to every use of 桁違い.
Does 優勝者の記録は桁違いだった。 establish a difference of exactly ten times?
Show the answer and why
No. It assesses a striking difference. The actual records and comparison base are needed to calculate a multiplier.